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Volumn 2, Issue , 2002, Pages 983-1055

Chapter 18 Stability of travelling waves

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EID: 67649363651     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80039-X     Document Type: Chapter
Times cited : (433)

References (193)
  • 2
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • Alexander J.C., Gardner R.A., and Jones C.K.R.T. A topological invariant arising in the stability analysis of travelling waves. J. Reine Angew. Math. 410 (1990) 167-212
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.C.1    Gardner, R.A.2    Jones, C.K.R.T.3
  • 3
    • 0001347737 scopus 로고
    • Existence and stability of asymptotically oscillatory triple pulses
    • Alexander J.C., and Jones C.K.R.T. Existence and stability of asymptotically oscillatory triple pulses. Z. Angew. Math. Phys. 44 (1993) 189-200
    • (1993) Z. Angew. Math. Phys. , vol.44 , pp. 189-200
    • Alexander, J.C.1    Jones, C.K.R.T.2
  • 4
    • 84961472729 scopus 로고
    • Existence and stability of asymptotically oscillatory double pulses
    • Alexander J.C., and Jones C.K.R.T. Existence and stability of asymptotically oscillatory double pulses. J. Reine Angew. Math. 446 (1994) 49-79
    • (1994) J. Reine Angew. Math. , vol.446 , pp. 49-79
    • Alexander, J.C.1    Jones, C.K.R.T.2
  • 5
    • 0011479633 scopus 로고
    • Linear instability of solitary waves of a Boussinesq-type equation: A com-puter assisted computation
    • Alexander J.C., and Sachs R.L. Linear instability of solitary waves of a Boussinesq-type equation: A com-puter assisted computation. Nonlinear World 2 (1995) 471-507
    • (1995) Nonlinear World , vol.2 , pp. 471-507
    • Alexander, J.C.1    Sachs, R.L.2
  • 9
    • 0002538743 scopus 로고
    • Invariant manifolds for semilinear partial differential equations
    • Bates P.W., and Jones C.K.R.T. Invariant manifolds for semilinear partial differential equations. Dynamics Reported 2 (1989) 1-38
    • (1989) Dynamics Reported , vol.2 , pp. 1-38
    • Bates, P.W.1    Jones, C.K.R.T.2
  • 10
    • 0000363750 scopus 로고
    • The stability of solitary waves
    • Benjamin T.B. The stability of solitary waves. Proc. Roy. Soc. London A 328 (1972) 153-183
    • (1972) Proc. Roy. Soc. London A , vol.328 , pp. 153-183
    • Benjamin, T.B.1
  • 11
    • 0002433039 scopus 로고
    • Global bifurcations and their numerical computation
    • Roose D., Spence A., and Dier B.D. (Eds), Kluwer, Dordrecht
    • Beyn W.-J. Global bifurcations and their numerical computation. In: Roose D., Spence A., and Dier B.D. (Eds). Continuation and Bifurcations: Numerical Techniques and Applications (1990), Kluwer, Dordrecht 169-181
    • (1990) Continuation and Bifurcations: Numerical Techniques and Applications , pp. 169-181
    • Beyn, W.-J.1
  • 12
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • Beyn W.-J. The numerical computation of connecting orbits in dynamical systems. IMA J. Numer. Anal. 10 (1990) 379-405
    • (1990) IMA J. Numer. Anal. , vol.10 , pp. 379-405
    • Beyn, W.-J.1
  • 13
    • 0032678491 scopus 로고    scopus 로고
    • Stability of traveling waves: Dichotomies and eigenvalue conditions on finite intervals
    • Beyn W.-J., and Lorenz J. Stability of traveling waves: Dichotomies and eigenvalue conditions on finite intervals. Numer. Funct. Anal. Opt. 20 (1999) 201-244
    • (1999) Numer. Funct. Anal. Opt. , vol.20 , pp. 201-244
    • Beyn, W.-J.1    Lorenz, J.2
  • 15
    • 0000961428 scopus 로고
    • Stability of the in-phase travelling wave solution in a pair of coupled nerve fibers
    • Bose A., and Jones C.K.R.T. Stability of the in-phase travelling wave solution in a pair of coupled nerve fibers. Indiana Univ. Math. J. 44 (1995) 189-220
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 189-220
    • Bose, A.1    Jones, C.K.R.T.2
  • 16
    • 0029656921 scopus 로고    scopus 로고
    • Absolute and convective instabilities of spatially periodic flows
    • Brevdo L., and Bridges T.J. Absolute and convective instabilities of spatially periodic flows. Philos. Trans. Roy. Soc. London A 354 (1996) 1027-1064
    • (1996) Philos. Trans. Roy. Soc. London A , vol.354 , pp. 1027-1064
    • Brevdo, L.1    Bridges, T.J.2
  • 17
    • 21144479301 scopus 로고
    • Renormalization group and the Ginzburg-Landau equation
    • Bricmont J., and Kupiainen A. Renormalization group and the Ginzburg-Landau equation. Comm. Math. Phys. 150 (1992) 193-208
    • (1992) Comm. Math. Phys. , vol.150 , pp. 193-208
    • Bricmont, J.1    Kupiainen, A.2
  • 18
    • 21344495443 scopus 로고
    • Stability of moving fronts in the Ginzburg-Landau equation
    • Bricmont J., and Kupiainen A. Stability of moving fronts in the Ginzburg-Landau equation. Comm. Math. Phys. 159 (1994) 287-318
    • (1994) Comm. Math. Phys. , vol.159 , pp. 287-318
    • Bricmont, J.1    Kupiainen, A.2
  • 19
    • 84990739185 scopus 로고
    • Renormalization group and asymptotics of solutions of nonlinear parabolic equations
    • Bricmont J., Kupiainen A., and Lin G. Renormalization group and asymptotics of solutions of nonlinear parabolic equations. Comm. Pure Appl. Math. 47 (1994) 893-922
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 893-922
    • Bricmont, J.1    Kupiainen, A.2    Lin, G.3
  • 20
    • 0004500194 scopus 로고    scopus 로고
    • Universal geometric condition for the transverse instability of solitary waves
    • Bridges T.J. Universal geometric condition for the transverse instability of solitary waves. Phys. Rev. Lett. 84 (2000) 2614-2617
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 2614-2617
    • Bridges, T.J.1
  • 21
    • 33746421439 scopus 로고    scopus 로고
    • Unstable eigenvalues and the linearization about solitary waves and fronts with symmetry
    • Bridges T.J., and Derks G. Unstable eigenvalues and the linearization about solitary waves and fronts with symmetry. Proc. Roy. Soc. London A 455 (1999) 2427-2469
    • (1999) Proc. Roy. Soc. London A , vol.455 , pp. 2427-2469
    • Bridges, T.J.1    Derks, G.2
  • 22
    • 0035582791 scopus 로고    scopus 로고
    • The symplectic Evans matrix, and the instability of solitary waves and fronts with symmetry
    • Bridges T.J., and Derks G. The symplectic Evans matrix, and the instability of solitary waves and fronts with symmetry. Arch. Rat. Mech. Anal. 156 (2001) 1-87
    • (2001) Arch. Rat. Mech. Anal. , vol.156 , pp. 1-87
    • Bridges, T.J.1    Derks, G.2
  • 23
    • 0012945442 scopus 로고
    • A proof of the Benjamin-Feir instability
    • Bridges T.J., and Mielke A. A proof of the Benjamin-Feir instability. Arch. Rat. Mech. Anal. 133 (1995) 145-198
    • (1995) Arch. Rat. Mech. Anal. , vol.133 , pp. 145-198
    • Bridges, T.J.1    Mielke, A.2
  • 25
    • 53349120754 scopus 로고    scopus 로고
    • Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
    • Buffoni B., Champneys A.R., and Toland J.F. Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system. J. Dynamics Differential Equations 8 (1996) 221-279
    • (1996) J. Dynamics Differential Equations , vol.8 , pp. 221-279
    • Buffoni, B.1    Champneys, A.R.2    Toland, J.F.3
  • 27
    • 21844508998 scopus 로고
    • Subsidiary homoclinic orbits to a s addle-focus for reversible systems
    • Champneys A.R. Subsidiary homoclinic orbits to a s addle-focus for reversible systems. Internat. J. Bifur-cation Chaos 4 (1994) 1447-1482
    • (1994) Internat. J. Bifur-cation Chaos , vol.4 , pp. 1447-1482
    • Champneys, A.R.1
  • 28
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homo-clinic bifurcations
    • Champneys A.R., and Kuznetsov Y.A. Numerical detection and continuation of codimension-two homo-clinic bifurcations. Internat. J. Bifurcation Chaos 4 (1994) 795-822
    • (1994) Internat. J. Bifurcation Chaos , vol.4 , pp. 795-822
    • Champneys, A.R.1    Kuznetsov, Y.A.2
  • 30
    • 0000128696 scopus 로고    scopus 로고
    • Local stability theory of solitary pulses in an active medium
    • Chang H.-C., Demekhin E.A., and Kopelevich D.I. Local stability theory of solitary pulses in an active medium. Phys. D 97 (1996) 353-375
    • (1996) Phys. D , vol.97 , pp. 353-375
    • Chang, H.-C.1    Demekhin, E.A.2    Kopelevich, D.I.3
  • 31
    • 0032139836 scopus 로고    scopus 로고
    • Generation and suppression of radiation by solitary pulses
    • Chang H.-C., Demekhin E.A., and Kopelevich D.I. Generation and suppression of radiation by solitary pulses. SIAM J. Appl. Math. 58 (1998) 1246-1277
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1246-1277
    • Chang, H.-C.1    Demekhin, E.A.2    Kopelevich, D.I.3
  • 35
    • 0040953231 scopus 로고
    • Diffusive repair for the Ginzburg-Landau equation
    • Collet R., Eckmann J.-R., and Epstein H. Diffusive repair for the Ginzburg-Landau equation. Helv. Phys. Acta 65 (1992) 56-92
    • (1992) Helv. Phys. Acta , vol.65 , pp. 56-92
    • Collet, R.1    Eckmann, J.-R.2    Epstein, H.3
  • 36
    • 0002709196 scopus 로고
    • Dichotomies in Stability Theory
    • Springer, Berlin
    • Coppel W.A. Dichotomies in Stability Theory. Lecture Notes in Math. Vol. 629 (1978), Springer, Berlin
    • (1978) Lecture Notes in Math. , vol.629
    • Coppel, W.A.1
  • 37
    • 48249136459 scopus 로고    scopus 로고
    • Stability of travelling-wave solutions for reaction-diffusion-convection systems
    • Crooks E.C.M. Stability of travelling-wave solutions for reaction-diffusion-convection systems. Topol. Methods Nonlinear Anal. 16 (2000) 37-63
    • (2000) Topol. Methods Nonlinear Anal. , vol.16 , pp. 37-63
    • Crooks, E.C.M.1
  • 39
    • 0000775150 scopus 로고
    • The bifurcations of countable connections from a twisted heteroclinic loop
    • Deng B. The bifurcations of countable connections from a twisted heteroclinic loop. SIAM J. Math. Anal. 22 (1991) 653-679
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 653-679
    • Deng, B.1
  • 40
    • 0000997882 scopus 로고
    • The existence of infinitely many travelling front and back waves in the FitzHugh-Nagumo equa-tions
    • Deng B. The existence of infinitely many travelling front and back waves in the FitzHugh-Nagumo equa-tions. SIAM J. Math. Anal. 22 (1991) 1631-1650
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1631-1650
    • Deng, B.1
  • 41
    • 0001630378 scopus 로고
    • On Shilnikov's homoclinic-saddle-focus theorem
    • Deng B. On Shilnikov's homoclinic-saddle-focus theorem. J. Differential Equations 102 (1993) 305-329
    • (1993) J. Differential Equations , vol.102 , pp. 305-329
    • Deng, B.1
  • 42
    • 0000107832 scopus 로고
    • Homoclinic orbits in Hamiltonian systems
    • Devaney R.L. Homoclinic orbits in Hamiltonian systems. J. Differential Equations 21 (1976) 431-438
    • (1976) J. Differential Equations , vol.21 , pp. 431-438
    • Devaney, R.L.1
  • 43
    • 0033489572 scopus 로고    scopus 로고
    • Nonlinear gravity and capillary-gravity waves
    • Dias F., and Kharif C. Nonlinear gravity and capillary-gravity waves. Ann. Rev. Fluid. Mech. 31 (1999) 301-346
    • (1999) Ann. Rev. Fluid. Mech. , vol.31 , pp. 301-346
    • Dias, F.1    Kharif, C.2
  • 45
    • 0005468518 scopus 로고    scopus 로고
    • Stability analysis of singular patterns in the 1D Gray-Scott model: A matched asymptotics approach
    • Doelman A., Gardner R.A., and Kaper T.J. Stability analysis of singular patterns in the 1D Gray-Scott model: A matched asymptotics approach. Phys. D 122 (1998) 1-36
    • (1998) Phys. D , vol.122 , pp. 1-36
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.J.3
  • 46
    • 85087535683 scopus 로고    scopus 로고
    • A stability index analysis of 1-D patterns of the 1D Gray-Scott model
    • to be published
    • A. Doelman, R.A. Gardner and T.J. Kaper, A stability index analysis of 1-D patterns of the 1D Gray-Scott model, Mem. Amer. Math. Soc. (to be published).
    • Mem. Amer. Math. Soc
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.J.3
  • 47
    • 0000132086 scopus 로고    scopus 로고
    • Large stable pulse solutions in reaction-diffusion equations
    • (in press)
    • (in press). Doelman A., Gardner R.A., and Kaper T.J. Large stable pulse solutions in reaction-diffusion equations. Indiana Univ. Math. J. 50 (2001)
    • (2001) Indiana Univ. Math. J. , vol.50
    • Doelman, A.1    Gardner, R.A.2    Kaper, T.J.3
  • 48
    • 0039149429 scopus 로고    scopus 로고
    • Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
    • Ebert U., and Saarloos W.v. Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts. Phys. D 146 (2000) 1-99
    • (2000) Phys. D , vol.146 , pp. 1-99
    • Ebert, U.1    Saarloos, W.v.2
  • 49
    • 34249762638 scopus 로고
    • The nonlinear stability of front solutions for parabolic partial differential equations
    • Eckmann J.-P., and Wayne C.E. The nonlinear stability of front solutions for parabolic partial differential equations. Comm. Math. Phys. 161 (1994) 323-334
    • (1994) Comm. Math. Phys. , vol.161 , pp. 323-334
    • Eckmann, J.-P.1    Wayne, C.E.2
  • 50
    • 0031325061 scopus 로고    scopus 로고
    • Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation
    • Eckmann J.-P., Wayne C.E., and Wittwer P. Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation. Comm. Math. Phys. 190 (1997) 173-211
    • (1997) Comm. Math. Phys. , vol.190 , pp. 173-211
    • Eckmann, J.-P.1    Wayne, C.E.2    Wittwer, P.3
  • 51
    • 67649367897 scopus 로고    scopus 로고
    • The motion of weakly interacting pulses in reaction-diffusion systems
    • to be published
    • S.-I. Ei, The motion of weakly interacting pulses in reaction-diffusion systems, J. Dynamics Differential Equations (to be published).
    • J. Dynamics Differential Equations
    • Ei, S.-I.1
  • 53
    • 0004029354 scopus 로고    scopus 로고
    • An Evans function analysis of the stability of periodic travelling wave solutions of the FitzHugh-Nagumo system
    • University of Massachusetts, Amherst
    • Eszter E.G. An Evans function analysis of the stability of periodic travelling wave solutions of the FitzHugh-Nagumo system. Ph.D. thesis (1999), University of Massachusetts, Amherst
    • (1999) Ph.D. thesis
    • Eszter, E.G.1
  • 54
    • 0001472246 scopus 로고
    • Nerve axon equations (iii) : Stability of the nerve impulses
    • Evans J. Nerve axon equations (iii) : Stability of the nerve impulses. Indiana Univ. Math. J. 22 (1972) 577-594
    • (1972) Indiana Univ. Math. J. , vol.22 , pp. 577-594
    • Evans, J.1
  • 55
    • 0342924582 scopus 로고    scopus 로고
    • Global pathfollowing of homoclinic orbits in two-parameter flows
    • Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds), Longman, Harlow
    • Fiedler B. Global pathfollowing of homoclinic orbits in two-parameter flows. In: Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds). Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Pitman Res. Notes in Math. Ser. Vol. 352 (1996), Longman, Harlow 79-145
    • (1996) Pitman Res. Notes in Math. Ser. , vol.352 , pp. 79-145
    • Fiedler, B.1
  • 56
    • 0000384434 scopus 로고    scopus 로고
    • Bifurcations from relative equilibria of noncompact group actions: Skew products, meanders, and drifts
    • Fiedler B., Sandstede B., Scheel A., and Wulff C. Bifurcations from relative equilibria of noncompact group actions: Skew products, meanders, and drifts. Doc. Math. 1 (1996) 479-505
    • (1996) Doc. Math. , vol.1 , pp. 479-505
    • Fiedler, B.1    Sandstede, B.2    Scheel, A.3    Wulff, C.4
  • 57
    • 0032210477 scopus 로고    scopus 로고
    • Large patterns of elliptic systems in infinite cylinders
    • Fiedler B., Scheel A., and Vishik M.I. Large patterns of elliptic systems in infinite cylinders. J. Math. Pures Appl. 77 (1998) 879-907
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 879-907
    • Fiedler, B.1    Scheel, A.2    Vishik, M.I.3
  • 58
    • 0010050153 scopus 로고    scopus 로고
    • Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions
    • Fiedler B., and Turaev D. Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions. Arch. Rat. Mech. Anal. 145 (1998) 129-159
    • (1998) Arch. Rat. Mech. Anal. , vol.145 , pp. 129-159
    • Fiedler, B.1    Turaev, D.2
  • 59
    • 67649321646 scopus 로고    scopus 로고
    • Patterns formation in gradient systems
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Fife P.C. Patterns formation in gradient systems. In: Fiedler B. (Ed). Handbook of Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 677-722
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 677-722
    • Fife, P.C.1
  • 60
    • 0000156777 scopus 로고    scopus 로고
    • Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system
    • Focant S., and Gallay T. Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system. Phys. D 120 (1998) 346-368
    • (1998) Phys. D , vol.120 , pp. 346-368
    • Focant, S.1    Gallay, T.2
  • 61
    • 0026170304 scopus 로고
    • Numerical computation and continuation of invariant manifolds connect-ing fixed points
    • Friedman M.J., and Doedel E.J. Numerical computation and continuation of invariant manifolds connect-ing fixed points. SIAM J. Numer. Anal. 28 (1991) 789-808
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 789-808
    • Friedman, M.J.1    Doedel, E.J.2
  • 62
    • 0001863910 scopus 로고
    • Slow-motion manifolds, dormant instability, and singular perturbations
    • Fusco G., and Hale J. Slow-motion manifolds, dormant instability, and singular perturbations. J. Dynamics Differential Equations 1 (1989) 75-94
    • (1989) J. Dynamics Differential Equations , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J.2
  • 63
    • 0001171846 scopus 로고
    • Local stability of critical fronts in nonlinear parabolic partial differential equations
    • Gallay T. Local stability of critical fronts in nonlinear parabolic partial differential equations. Nonlinear-ity 7 (1994) 741-764
    • (1994) Nonlinear-ity , vol.7 , pp. 741-764
    • Gallay, T.1
  • 64
    • 22444455115 scopus 로고    scopus 로고
    • Diffusive mixing of stable states in the Ginzburg-Landau equation
    • Gallay T., and Mielke A. Diffusive mixing of stable states in the Ginzburg-Landau equation. Comm. Math. Phys. 199 (1998) 71-97
    • (1998) Comm. Math. Phys. , vol.199 , pp. 71-97
    • Gallay, T.1    Mielke, A.2
  • 65
    • 0031490679 scopus 로고    scopus 로고
    • Stability of travelling waves for a damped hyperbolic equation
    • Gallay T., and Raugel G. Stability of travelling waves for a damped hyperbolic equation. Z. Angew. Math. Phys. 48 (1997) 451-479
    • (1997) Z. Angew. Math. Phys. , vol.48 , pp. 451-479
    • Gallay, T.1    Raugel, G.2
  • 66
    • 0034353685 scopus 로고    scopus 로고
    • Scaling variables and stability of hyperbolic fronts
    • Gallay T., and Raugel G. Scaling variables and stability of hyperbolic fronts. SIAM J. Math. Anal. 32 (2000) 1-29
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 1-29
    • Gallay, T.1    Raugel, G.2
  • 67
    • 46149141487 scopus 로고
    • Existence of multidimensional travelling wave solutions of an initial-boundary value prob-lem
    • Gardner R.A. Existence of multidimensional travelling wave solutions of an initial-boundary value prob-lem. J. Differential Equations 61 (1986) 335-379
    • (1986) J. Differential Equations , vol.61 , pp. 335-379
    • Gardner, R.A.1
  • 68
    • 0001307276 scopus 로고
    • On the structure of the spectra of periodic travelling waves
    • Gardner R.A. On the structure of the spectra of periodic travelling waves. J. Math. Pures Appl. 72 (1993) 415-439
    • (1993) J. Math. Pures Appl. , vol.72 , pp. 415-439
    • Gardner, R.A.1
  • 69
    • 0031285528 scopus 로고    scopus 로고
    • Spectral analysis of long wavelength periodic waves and applications
    • Gardner R.A. Spectral analysis of long wavelength periodic waves and applications. J. Reine Angew. Math. 491 (1997) 149-181
    • (1997) J. Reine Angew. Math. , vol.491 , pp. 149-181
    • Gardner, R.A.1
  • 70
    • 0000417982 scopus 로고
    • Traveling waves of a perturbed diffusion equation arising in a phase field model
    • Gardner R.A., and Jones C.K.R.T. Traveling waves of a perturbed diffusion equation arising in a phase field model. Indiana Univ. Math. J. 39 (1990) 1197-1222
    • (1990) Indiana Univ. Math. J. , vol.39 , pp. 1197-1222
    • Gardner, R.A.1    Jones, C.K.R.T.2
  • 71
    • 84966244631 scopus 로고
    • Stability of travelling wave solutions of diffusive predator-prey systems
    • Gardner R.A., and Jones C.K.R.T. Stability of travelling wave solutions of diffusive predator-prey systems. Trans. Amer. Math. Soc. 327 (1991) 465-524
    • (1991) Trans. Amer. Math. Soc. , vol.327 , pp. 465-524
    • Gardner, R.A.1    Jones, C.K.R.T.2
  • 72
    • 0040942605 scopus 로고    scopus 로고
    • The gap lemma and geometric criteria for instability of viscous shock profiles
    • Gardner R.A., and Zumbrun K. The gap lemma and geometric criteria for instability of viscous shock profiles. Comm. Pure Appl. Math. 51 (1998) 797-855
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 797-855
    • Gardner, R.A.1    Zumbrun, K.2
  • 73
    • 84974127826 scopus 로고
    • Subsidiary bifurcations near bifocal homoclinic orbits
    • Glendinning P. Subsidiary bifurcations near bifocal homoclinic orbits. Math. Proc. Cambridge Philos. Soc. 105 (1989) 597-605
    • (1989) Math. Proc. Cambridge Philos. Soc. , vol.105 , pp. 597-605
    • Glendinning, P.1
  • 74
    • 0000530394 scopus 로고    scopus 로고
    • Meandering of the spiral tip -an alternative approach
    • Golubitsky M., LeBlanc V., and Melbourne I. Meandering of the spiral tip -an alternative approach. J. Nonlinear Sci. 7 (1997) 557-586
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 557-586
    • Golubitsky, M.1    LeBlanc, V.2    Melbourne, I.3
  • 76
    • 84990623184 scopus 로고
    • Linearized instability for nonlinear Schrödinger and Klein-Gordon equations
    • Grillakis M. Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Comm. Pure Appl. Math. 41 (1988) 747-774
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 747-774
    • Grillakis, M.1
  • 77
    • 84990563336 scopus 로고
    • Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system
    • Grillakis M. Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system. Comm. Pure Appl. Math. 43 (1990) 299-333
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 299-333
    • Grillakis, M.1
  • 78
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry I
    • Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in the presence of symmetry I. J. Funct. Anal. 74 (1987) 160-197
    • (1987) J. Funct. Anal. , vol.74 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 79
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry II
    • Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in the presence of symmetry II. J. Funct. Anal. 94 (1990) 308-348
    • (1990) J. Funct. Anal. , vol.94 , pp. 308-348
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 81
    • 0001645343 scopus 로고
    • Spiral waves in reaction-diffusion equations
    • Hagan P.S. Spiral waves in reaction-diffusion equations. SIAM J. Appl. Math. 42 (1982) 762-786
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 762-786
    • Hagan, P.S.1
  • 82
    • 22244440263 scopus 로고    scopus 로고
    • Cascades of homoclinic orbits in reversible dynamical systems
    • Härterich J. Cascades of homoclinic orbits in reversible dynamical systems. Phys. D 112 (1998) 187-200
    • (1998) Phys. D , vol.112 , pp. 187-200
    • Härterich, J.1
  • 84
    • 0004192781 scopus 로고
    • Traveling waves for semilinear parabolic partial differential equations in cylindrical domains
    • University of Heidelberg
    • Heinze S. Traveling waves for semilinear parabolic partial differential equations in cylindrical domains. Ph.D. thesis (1989), University of Heidelberg
    • (1989) Ph.D. thesis
    • Heinze, S.1
  • 85
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, New York
    • Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. Vol. 804 (1981), Springer, New York
    • (1981) Lecture Notes in Math. , vol.804
    • Henry, D.1
  • 86
    • 0001559874 scopus 로고
    • The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
    • Homburg A.J., Kokubu H., and Krupa M. The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit. Ergodic Theory Dynamical Systems 14 (1994) 667-693
    • (1994) Ergodic Theory Dynamical Systems , vol.14 , pp. 667-693
    • Homburg, A.J.1    Kokubu, H.2    Krupa, M.3
  • 87
    • 43949099544 scopus 로고    scopus 로고
    • Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems
    • Ikeda H., and Ikeda T. Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems. J. Dynamics Differential Equations 12 (2000) 117-167
    • (2000) J. Dynamics Differential Equations , vol.12 , pp. 117-167
    • Ikeda, H.1    Ikeda, T.2
  • 88
    • 21344443135 scopus 로고    scopus 로고
    • Stability of traveling waves and a relation between the Evans function and the SLEP equation
    • Ikeda H., Nishiura Y., and Suzuki Y. Stability of traveling waves and a relation between the Evans function and the SLEP equation. J. Reine Angew. Math. 475 (1996) 1-37
    • (1996) J. Reine Angew. Math. , vol.475 , pp. 1-37
    • Ikeda, H.1    Nishiura, Y.2    Suzuki, Y.3
  • 90
    • 84967743294 scopus 로고
    • Stability of the travelling wave solution of the FitzHugh-Nagumo system
    • Jones C.K.R.T. Stability of the travelling wave solution of the FitzHugh-Nagumo system. Trans. Amer. Math. Soc. 286 (1984) 431-469
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.K.R.T.1
  • 91
    • 0002316532 scopus 로고
    • Geometric Singular Perturbation Theory
    • C.I.M.E. Lectures. Terme M. (Ed), Springer, Heidelberg
    • Jones C.K.R.T. Geometric Singular Perturbation Theory. In: Terme M. (Ed). C.I.M.E. Lectures. Lecture Notes in Math. Vol. 1609 (1995), Springer, Heidelberg
    • (1995) Lecture Notes in Math. , vol.1609
    • Jones, C.K.R.T.1
  • 92
    • 84990556253 scopus 로고
    • Stability of travelling waves for nonconvex scalar viscous conservation laws
    • Jones C.K.R.T., Gardner R.A., and Kapitula T. Stability of travelling waves for nonconvex scalar viscous conservation laws. Comm. Pure Appl. Math. 46 (1993) 505-526
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 505-526
    • Jones, C.K.R.T.1    Gardner, R.A.2    Kapitula, T.3
  • 93
    • 0001100679 scopus 로고
    • On the stability of travelling waves in weighted L∞ spaces
    • Kapitula T. On the stability of travelling waves in weighted L∞ spaces. J. Differential Equations 112 (1994) 179-215
    • (1994) J. Differential Equations , vol.112 , pp. 179-215
    • Kapitula, T.1
  • 94
    • 0002348146 scopus 로고    scopus 로고
    • Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrödinger equa-tion
    • Kapitula T. Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrödinger equa-tion. Phys. D 116 (1998) 95-120
    • (1998) Phys. D , vol.116 , pp. 95-120
    • Kapitula, T.1
  • 95
    • 0032622893 scopus 로고    scopus 로고
    • The Evans function and generalized Melnikov integrals
    • Kapitula T. The Evans function and generalized Melnikov integrals. SIAM J. Math. Anal. 30 (1999) 273-297
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 273-297
    • Kapitula, T.1
  • 96
    • 0033628312 scopus 로고    scopus 로고
    • Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
    • Kapitula T., and Rubin J. Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Nonlinearity 13 (2000) 77-112
    • (2000) Nonlinearity , vol.13 , pp. 77-112
    • Kapitula, T.1    Rubin, J.2
  • 97
    • 0002348145 scopus 로고    scopus 로고
    • Stability of bright solitary wave solutions to perturbed nonlinear Schrödinger equations
    • Kapitula T., and Sandstede B. Stability of bright solitary wave solutions to perturbed nonlinear Schrödinger equations. Phys. D 124 (1998) 58-103
    • (1998) Phys. D , vol.124 , pp. 58-103
    • Kapitula, T.1    Sandstede, B.2
  • 98
    • 0032355359 scopus 로고    scopus 로고
    • A novel instability mechanism for bright solitary-wave solutions to the cubic-quintic Ginzburg-Landau equation
    • Kapitula T., and Sandstede B. A novel instability mechanism for bright solitary-wave solutions to the cubic-quintic Ginzburg-Landau equation. J. Opt. Soc. Amer. B 15 (1998) 2757-2762
    • (1998) J. Opt. Soc. Amer. B , vol.15 , pp. 2757-2762
    • Kapitula, T.1    Sandstede, B.2
  • 99
    • 0004095143 scopus 로고
    • Kapral R., and Showalter K. (Eds), Kluwer, Dordrecht
    • In: Kapral R., and Showalter K. (Eds). Chemical Waves and Patterns (1995), Kluwer, Dordrecht
    • (1995) Chemical Waves and Patterns
  • 101
    • 49049138209 scopus 로고
    • Wave-solutions of reversible systems and applications
    • Kirchgässner K. Wave-solutions of reversible systems and applications. J. Differential Equations 45 (1982) 113-127
    • (1982) J. Differential Equations , vol.45 , pp. 113-127
    • Kirchgässner, K.1
  • 102
    • 44049118931 scopus 로고
    • On the nonlinear dynamics of travelling fronts
    • Kirchgässner K. On the nonlinear dynamics of travelling fronts. J. Differential Equations 96 (1992) 256-278
    • (1992) J. Differential Equations , vol.96 , pp. 256-278
    • Kirchgässner, K.1
  • 103
    • 0039093031 scopus 로고    scopus 로고
    • Stability of fronts for a KPP-system: The noncritical case
    • Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds), Longman, Harlow
    • Kirchgässner K., and Raugel G. Stability of fronts for a KPP-system: The noncritical case. In: Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds). Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Pitman Res. Notes in Math. Ser. Vol. 352 (1996), Longman, Harlow 147-208
    • (1996) Pitman Res. Notes in Math. Ser. , vol.352 , pp. 147-208
    • Kirchgässner, K.1    Raugel, G.2
  • 104
    • 0001002402 scopus 로고
    • Bifurcations to N-homoclinic orbits and N-periodic orbits in vector fields
    • Kisaka M., Kokubu H., and Oka H. Bifurcations to N-homoclinic orbits and N-periodic orbits in vector fields. J. Dynamics Differential Equations 5 (1993) 305-357
    • (1993) J. Dynamics Differential Equations , vol.5 , pp. 305-357
    • Kisaka, M.1    Kokubu, H.2    Oka, H.3
  • 106
    • 0030128338 scopus 로고    scopus 로고
    • Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers
    • Kutz J., and Kath W. Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers. SIAM J. Appl. Math. 56 (1996) 611-626
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 611-626
    • Kutz, J.1    Kath, W.2
  • 108
    • 0001043191 scopus 로고    scopus 로고
    • A stability analysis of fifth-order water wave models
    • Levandosky S.P. A stability analysis of fifth-order water wave models. Phys. D 125 (1999) 222-240
    • (1999) Phys. D , vol.125 , pp. 222-240
    • Levandosky, S.P.1
  • 109
    • 11544364689 scopus 로고    scopus 로고
    • Structural stability of nonground state traveling waves of coupled nonlinear Schrödinger equations
    • Li Y.A., and Promislow K. Structural stability of nonground state traveling waves of coupled nonlinear Schrödinger equations. Phys. D 124 (1998) 137-165
    • (1998) Phys. D , vol.124 , pp. 137-165
    • Li, Y.A.1    Promislow, K.2
  • 110
    • 0034347554 scopus 로고    scopus 로고
    • The mechanism of the polarizational mode instability in birefringent fiber optics
    • Li Y.A., and Promislow K. The mechanism of the polarizational mode instability in birefringent fiber optics. SIAM J. Math. Anal. 31 (2000) 1351-1373
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 1351-1373
    • Li, Y.A.1    Promislow, K.2
  • 111
    • 84972438215 scopus 로고
    • Using Melnikov's method to solve Shilnikov's problems
    • Lin X.-B. Using Melnikov's method to solve Shilnikov's problems. Proc. Roy. Soc. Edinburgh Sect. A 116 (1990) 295-325
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.116 , pp. 295-325
    • Lin, X.-B.1
  • 112
    • 23044526615 scopus 로고    scopus 로고
    • Construction and asymptotic stability of structurally stable internal layer solutions
    • Lin X.-B. Construction and asymptotic stability of structurally stable internal layer solutions. Trans. Amer. Math. Soc. 353 (2001) 2983-3043
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 2983-3043
    • Lin, X.-B.1
  • 113
    • 0000822594 scopus 로고    scopus 로고
    • Numerical computation of solitary waves in infinite cylindrical domains
    • Lord G.J., Peterhof D., Sandstede B., and Scheel A. Numerical computation of solitary waves in infinite cylindrical domains. SIAM J. Numer. Anal. 37 (2000) 1420-1454
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1420-1454
    • Lord, G.J.1    Peterhof, D.2    Sandstede, B.3    Scheel, A.4
  • 114
    • 0002247515 scopus 로고
    • Restricted quadratic forms and their application to bifurcation and stability in constrained variational principles
    • Maddocks J.H. Restricted quadratic forms and their application to bifurcation and stability in constrained variational principles. SIAM J. Math. Anal. 16 (1985) 47-68
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 47-68
    • Maddocks, J.H.1
  • 115
    • 67649377291 scopus 로고
    • Restricted quadratic forms and their application to bifurcation and stability in constrained variational principles
    • Maddocks J.H. Restricted quadratic forms and their application to bifurcation and stability in constrained variational principles. Errata 19 (1988) 1256-1257
    • (1988) Errata , vol.19 , pp. 1256-1257
    • Maddocks, J.H.1
  • 116
  • 117
    • 33746739797 scopus 로고
    • Constrained variational principles and stability in Hamiltonian systems
    • Hamiltonian Dynamical Systems, Springer, New York
    • Maddocks J.H., and Sachs R.L. Constrained variational principles and stability in Hamiltonian systems. Hamiltonian Dynamical Systems. IMA Vol. Math. Anal. Vol. 63 (1995), Springer, New York 231-264
    • (1995) IMA Vol. Math. Anal. , vol.63 , pp. 231-264
    • Maddocks, J.H.1    Sachs, R.L.2
  • 118
    • 0001883519 scopus 로고
    • Pattern formation in excitable media
    • Meron E. Pattern formation in excitable media. Phys. Reports 218 (1992) 1-66
    • (1992) Phys. Reports , vol.218 , pp. 1-66
    • Meron, E.1
  • 119
    • 0007068426 scopus 로고    scopus 로고
    • A spatial center manifold approach to steady bifurcations from spatially periodic patterns
    • Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds), Longman, Harlow
    • Mielke A. A spatial center manifold approach to steady bifurcations from spatially periodic patterns. In: Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds). Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Pitman Res. Notes in Math. Ser. Vol. 352 (1996), Longman, Harlow 209-262
    • (1996) Pitman Res. Notes in Math. Ser. , vol.352 , pp. 209-262
    • Mielke, A.1
  • 120
    • 0031549893 scopus 로고    scopus 로고
    • Instability and stability of rolls in the Swift-Hohenberg equation
    • Mielke A. Instability and stability of rolls in the Swift-Hohenberg equation. Comm. Math. Phys. 189 (1997) 829-853
    • (1997) Comm. Math. Phys. , vol.189 , pp. 829-853
    • Mielke, A.1
  • 121
    • 67649370945 scopus 로고    scopus 로고
    • The Ginzburg-Landau equation in its role as a modulation equation
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Mielke A. The Ginzburg-Landau equation in its role as a modulation equation. In: Fiedler B. (Ed). Handbook of Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 759-834
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 759-834
    • Mielke, A.1
  • 123
    • 0031533042 scopus 로고    scopus 로고
    • An extension of the stability index for travelling wave solutions and its application to bifurcations
    • Nii S. An extension of the stability index for travelling wave solutions and its application to bifurcations. SIAM J. Math. Anal. 28 (1997) 402-433
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 402-433
    • Nii, S.1
  • 124
    • 3042538112 scopus 로고    scopus 로고
    • Stability of travelling multiple-front (multiple-back) wave solutions of the FitzHugh-Nagumo equa-tions
    • Nii S. Stability of travelling multiple-front (multiple-back) wave solutions of the FitzHugh-Nagumo equa-tions. SIAM J. Math. Anal. 28 (1997) 1094-1112
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 1094-1112
    • Nii, S.1
  • 125
    • 0039773021 scopus 로고    scopus 로고
    • A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations
    • Nii S. A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations. J. Dynamics Differential Equations 11 (1999) 515-555
    • (1999) J. Dynamics Differential Equations , vol.11 , pp. 515-555
    • Nii, S.1
  • 126
    • 0345848729 scopus 로고    scopus 로고
    • Accumulation of eigenvalues in a stability problem
    • Nii S. Accumulation of eigenvalues in a stability problem. Phys. D 142 (2000) 70-86
    • (2000) Phys. D , vol.142 , pp. 70-86
    • Nii, S.1
  • 127
    • 67649357810 scopus 로고    scopus 로고
    • S. Nii and B. Sandstede, On the connection between the geometry and stability of multi-bump pulses arising in homoclinic flip bifurcations in preparati
    • S. Nii and B. Sandstede, On the connection between the geometry and stability of multi-bump pulses arising in homoclinic flip bifurcations (in preparati
  • 128
    • 0002882425 scopus 로고
    • Coexistence of infinitely many stable solutions to reaction-diffusion systems in the singular limit
    • Nishiura Y. Coexistence of infinitely many stable solutions to reaction-diffusion systems in the singular limit. Dynamics Reported 3 (1994) 25-103
    • (1994) Dynamics Reported , vol.3 , pp. 25-103
    • Nishiura, Y.1
  • 129
    • 0000988067 scopus 로고
    • Stability of singularly perturbed solutions to systems of reaction-diffusion equa-tions
    • Nishiura Y., and Fujii H. Stability of singularly perturbed solutions to systems of reaction-diffusion equa-tions. SIAM J. Math. Anal. 18 (1987) 1726-1770
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 1726-1770
    • Nishiura, Y.1    Fujii, H.2
  • 130
    • 0013322639 scopus 로고
    • Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion equations
    • Nishiura Y., Mimura M., Ikeda H., and Fujii H. Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion equations. SIAM J. Appl. Math. 49 (1990) 85-122
    • (1990) SIAM J. Appl. Math. , vol.49 , pp. 85-122
    • Nishiura, Y.1    Mimura, M.2    Ikeda, H.3    Fujii, H.4
  • 131
    • 0040333932 scopus 로고    scopus 로고
    • Stable bound states of pulses in an excitable medium
    • Or-Guil M., Kevrekidis I.G., and Bär M. Stable bound states of pulses in an excitable medium. Phys. D 135 (2000) 154-174
    • (2000) Phys. D , vol.135 , pp. 154-174
    • Or-Guil, M.1    Kevrekidis, I.G.2    Bär, M.3
  • 132
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • Palmer K.J. Exponential dichotomies and transversal homoclinic points. J. Differential Equations 55 (1984) 225-256
    • (1984) J. Differential Equations , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 133
    • 84968484465 scopus 로고
    • Exponential dichotomies and Fredholm operators
    • Palmer K.J. Exponential dichotomies and Fredholm operators. Proc. Amer. Math. Soc. 104 (1988) 149-156
    • (1988) Proc. Amer. Math. Soc. , vol.104 , pp. 149-156
    • Palmer, K.J.1
  • 135
  • 136
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • Pego R., and Weinstein M. Asymptotic stability of solitary waves. Comm. Math. Phys. 164 (1994) 305-349
    • (1994) Comm. Math. Phys. , vol.164 , pp. 305-349
    • Pego, R.1    Weinstein, M.2
  • 137
    • 0039573710 scopus 로고    scopus 로고
    • Convective linear stability of solitary waves for Boussinesq equations
    • Pego R., and Weinstein M. Convective linear stability of solitary waves for Boussinesq equations. Stud. Appl. Math. 99 (1997) 311-375
    • (1997) Stud. Appl. Math. , vol.99 , pp. 311-375
    • Pego, R.1    Weinstein, M.2
  • 138
    • 0001224746 scopus 로고    scopus 로고
    • Exponential dichotomies for solitary-wave solutions of semilin-ear elliptic equations on infinite cylinders
    • Peterhof D., Sandstede B., and Scheel A. Exponential dichotomies for solitary-wave solutions of semilin-ear elliptic equations on infinite cylinders. J. Differential Equations 140 (1997) 266-308
    • (1997) J. Differential Equations , vol.140 , pp. 266-308
    • Peterhof, D.1    Sandstede, B.2    Scheel, A.3
  • 140
    • 0007312917 scopus 로고    scopus 로고
    • Stability of fronts for a KPP-system II: The critical case
    • Raugel G., and Kirchgässner K. Stability of fronts for a KPP-system II: The critical case. J. Differential Equations 146 (1998) 399-456
    • (1998) J. Differential Equations , vol.146 , pp. 399-456
    • Raugel, G.1    Kirchgässner, K.2
  • 141
    • 0028695631 scopus 로고
    • Pseudospectra of the convection-diffusion operator
    • Reddy S.C., and Trefethen L.N. Pseudospectra of the convection-diffusion operator. SIAM J. Appl. Math. 54 (1994) 1634-1649
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1634-1649
    • Reddy, S.C.1    Trefethen, L.N.2
  • 142
    • 0030509749 scopus 로고    scopus 로고
    • Global stability of traveling fronts and convergence to-wards stacked families of waves in monotone parabolic systems
    • Roquejoffre J.-M., Terman D., and Volpert V.A. Global stability of traveling fronts and convergence to-wards stacked families of waves in monotone parabolic systems. SIAM J. Math. Anal. 27 (1996) 1261-1269
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1261-1269
    • Roquejoffre, J.-M.1    Terman, D.2    Volpert, V.A.3
  • 143
    • 12244273201 scopus 로고    scopus 로고
    • Stability bifurcations, and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system
    • Rubin J.E. Stability bifurcations, and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system. Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 1033-1079
    • (1999) Proc. Roy. Soc. Edinburgh Sect. A , vol.129 , pp. 1033-1079
    • Rubin, J.E.1
  • 144
    • 0003567524 scopus 로고
    • Verzweigungstheorie homokliner Verdopplungen
    • University of Stuttgart
    • Sandstede B. Verzweigungstheorie homokliner Verdopplungen. Ph.D. thesis (1993), University of Stuttgart
    • (1993) Ph.D. thesis
    • Sandstede, B.1
  • 145
    • 0031485993 scopus 로고    scopus 로고
    • Convergence estimates for the numerical approximation of homoclinic solutions
    • Sandstede B. Convergence estimates for the numerical approximation of homoclinic solutions. IMA J. Numer. Anal. 17 (1997) 437-462
    • (1997) IMA J. Numer. Anal. , vol.17 , pp. 437-462
    • Sandstede, B.1
  • 146
    • 3142624970 scopus 로고    scopus 로고
    • Instability of localized buckling modes in a one-dimensional strut model
    • Sandstede B. Instability of localized buckling modes in a one-dimensional strut model. Philos. Trans. Roy. Soc. London A 355 (1997) 2083-2097
    • (1997) Philos. Trans. Roy. Soc. London A , vol.355 , pp. 2083-2097
    • Sandstede, B.1
  • 147
    • 21944451412 scopus 로고    scopus 로고
    • Stability of multiple-pulse solutions
    • Sandstede B. Stability of multiple-pulse solutions. Trans. Amer. Math. Soc. 350 (1998) 429-472
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 429-472
    • Sandstede, B.1
  • 148
    • 0032338132 scopus 로고    scopus 로고
    • Stability of N-fronts bifurcating from a twisted heteroclinic loop and an application to the FitzHugh-Nagumo equation
    • Sandstede B. Stability of N-fronts bifurcating from a twisted heteroclinic loop and an application to the FitzHugh-Nagumo equation. SIAM J. Math. Anal. 29 (1998) 183-207
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 183-207
    • Sandstede, B.1
  • 151
    • 0031192318 scopus 로고    scopus 로고
    • Existence and stability ofn-pulses on optical fibers with phase-sensitive amplifiers
    • Sandstede B., Alexander J.C., and Jones C.K.R.T. Existence and stability ofn-pulses on optical fibers with phase-sensitive amplifiers. Phys. D 106 (1997) 167-206
    • (1997) Phys. D , vol.106 , pp. 167-206
    • Sandstede, B.1    Alexander, J.C.2    Jones, C.K.R.T.3
  • 152
    • 67649309333 scopus 로고    scopus 로고
    • Stability analysis of travelling waves in nonlocal equations and an application to modelocked pulses
    • Preprint
    • B. Sandstede, T. Kapitula and J. Kutz, Stability analysis of travelling waves in nonlocal equations and an application to modelocked pulses, Preprint.
    • Sandstede, B.1    Kapitula, T.2    Kutz, J.3
  • 153
    • 22844455596 scopus 로고    scopus 로고
    • Essential instability of pulses and bifurcations to modulated travelling waves
    • Sandstede B., and Scheel A. Essential instability of pulses and bifurcations to modulated travelling waves. Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 1263-1290
    • (1999) Proc. Roy. Soc. Edinburgh Sect. A , vol.129 , pp. 1263-1290
    • Sandstede, B.1    Scheel, A.2
  • 154
    • 23044518849 scopus 로고    scopus 로고
    • Spectral stability of modulated travelling waves bifurcating near essential instabilities
    • Sandstede B., and Scheel A. Spectral stability of modulated travelling waves bifurcating near essential instabilities. Proc. Roy. Soc. Edinburgh Sect. A 130 (2000) 419-448
    • (2000) Proc. Roy. Soc. Edinburgh Sect. A , vol.130 , pp. 419-448
    • Sandstede, B.1    Scheel, A.2
  • 155
    • 0034258264 scopus 로고    scopus 로고
    • Gluing unstable fronts and backs together can produce stable pulses
    • Sandstede B., and Scheel A. Gluing unstable fronts and backs together can produce stable pulses. Nonlinearity 13 (2000) 1465-1482
    • (2000) Nonlinearity , vol.13 , pp. 1465-1482
    • Sandstede, B.1    Scheel, A.2
  • 156
    • 0346686985 scopus 로고    scopus 로고
    • Absolute and convective instabilities of waves on unbounded and large bounded domains
    • Sandstede B., and Scheel A. Absolute and convective instabilities of waves on unbounded and large bounded domains. Phys. D 145 (2000) 233-277
    • (2000) Phys. D , vol.145 , pp. 233-277
    • Sandstede, B.1    Scheel, A.2
  • 157
    • 0035343506 scopus 로고    scopus 로고
    • On the stability of periodic travelling waves with large spatial period
    • Sandstede B., and Scheel A. On the stability of periodic travelling waves with large spatial period. J. Differential Equations 172 (2001) 134-188
    • (2001) J. Differential Equations , vol.172 , pp. 134-188
    • Sandstede, B.1    Scheel, A.2
  • 158
    • 85046908776 scopus 로고    scopus 로고
    • On the structure of spectra of modulated travelling waves
    • in press
    • B. Sandstede and A. Scheel, On the structure of spectra of modulated travelling waves, Math. Nachr. (in press).
    • Math. Nachr
    • Sandstede, B.1    Scheel, A.2
  • 159
    • 0035297089 scopus 로고    scopus 로고
    • Essential instabilities of fronts: Bifurcation, and bifurcation failure
    • Sandstede B., and Scheel A. Essential instabilities of fronts: Bifurcation, and bifurcation failure. Dynamical Systems 16 (2001) 1-28
    • (2001) Dynamical Systems , vol.16 , pp. 1-28
    • Sandstede, B.1    Scheel, A.2
  • 160
    • 0034506295 scopus 로고    scopus 로고
    • Absolute versus convective instability of spiral waves
    • Sandstede B., and Scheel A. Absolute versus convective instability of spiral waves. Phys. Rev. E 62 (2000) 7708-7714
    • (2000) Phys. Rev. E , vol.62 , pp. 7708-7714
    • Sandstede, B.1    Scheel, A.2
  • 161
    • 0031581236 scopus 로고    scopus 로고
    • Dynamics of spiral waves on unbounded domains using center-manifold reductions
    • Sandstede B., Scheel A., and Wulff C. Dynamics of spiral waves on unbounded domains using center-manifold reductions. J. Differential Equations 141 (1997) 122-149
    • (1997) J. Differential Equations , vol.141 , pp. 122-149
    • Sandstede, B.1    Scheel, A.2    Wulff, C.3
  • 162
    • 0000446211 scopus 로고    scopus 로고
    • Bifurcations and dynamics of spiral waves
    • Sandstede B., Scheel A., and Wulff C. Bifurcations and dynamics of spiral waves. J. Nonlinear Sci. 9 (1999) 439-478
    • (1999) J. Nonlinear Sci. , vol.9 , pp. 439-478
    • Sandstede, B.1    Scheel, A.2    Wulff, C.3
  • 163
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • Sattinger D.H. On the stability of waves of nonlinear parabolic systems. Adv. Math. 22 (1976) 312-355
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.H.1
  • 164
    • 0039938860 scopus 로고
    • L-perturbations of periodic equilibria of reaction-diffusion systems
    • Scarpellini B. L-perturbations of periodic equilibria of reaction-diffusion systems. Nonlinear Differen-tial Equations Appl. 1 (1994) 281-311
    • (1994) Nonlinear Differen-tial Equations Appl. , vol.1 , pp. 281-311
    • Scarpellini, B.1
  • 165
    • 0039938859 scopus 로고
    • The principle of linearized instability for space-periodic equilibria of Navier-Stokes on an infinite plate
    • Scarpellini B. The principle of linearized instability for space-periodic equilibria of Navier-Stokes on an infinite plate. Analysis 15 (1995) 359-391
    • (1995) Analysis , vol.15 , pp. 359-391
    • Scarpellini, B.1
  • 166
    • 0032361995 scopus 로고    scopus 로고
    • Bifurcation to spiral waves in reaction-diffusion systems
    • Scheel A. Bifurcation to spiral waves in reaction-diffusion systems. SIAM J. Math. Anal. 29 (1998) 1399-1418
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1399-1418
    • Scheel, A.1
  • 167
    • 0030560044 scopus 로고    scopus 로고
    • Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
    • Schneider G. Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation. Comm. Math. Phys. 178 (1996) 679-702
    • (1996) Comm. Math. Phys. , vol.178 , pp. 679-702
    • Schneider, G.1
  • 168
    • 0032344332 scopus 로고    scopus 로고
    • Nonlinear stability of Taylor vortices in infinite cylinders
    • Schneider G. Nonlinear stability of Taylor vortices in infinite cylinders. Arch. Rat. Mech. Anal. 144 (1998) 121-200
    • (1998) Arch. Rat. Mech. Anal. , vol.144 , pp. 121-200
    • Schneider, G.1
  • 169
    • 0009334519 scopus 로고    scopus 로고
    • Nonlinear diffusive stability of spatially periodic solutions - abstract theorem and higher space dimensions
    • Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems. Sendai, 1997
    • Schneider G. Nonlinear diffusive stability of spatially periodic solutions - abstract theorem and higher space dimensions. Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems. Sendai, 1997. Tohoku Math. Publ. Vol. 8 (1998) 159-167
    • (1998) Tohoku Math. Publ. , vol.8 , pp. 159-167
    • Schneider, G.1
  • 170
    • 0033734287 scopus 로고    scopus 로고
    • Existence and stability of modulating pulse-solutions in a phenomenological model of non-linear optics
    • Schneider G. Existence and stability of modulating pulse-solutions in a phenomenological model of non-linear optics. Phys. D 140 (2000) 283-293
    • (2000) Phys. D , vol.140 , pp. 283-293
    • Schneider, G.1
  • 171
    • 0001234956 scopus 로고
    • A case of the existence of a countable number of periodic motions
    • Shilnikov L.P. A case of the existence of a countable number of periodic motions. Soviet Math. Dokl. 6 (1965) 163-166
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 163-166
    • Shilnikov, L.P.1
  • 173
    • 3142589149 scopus 로고    scopus 로고
    • Theme issue on "Localisation and solitary waves in solid mechanics". Philos. Trans. Roy. Soc. London A 355 (1997)
    • (1997) Philos. Trans. Roy. Soc. London A , vol.355
  • 174
    • 67649330332 scopus 로고    scopus 로고
    • Theme issue on "Statics and dynamics of localisation phenomena". Nonlinear Dynamics 21 (2000)
    • (2000) Nonlinear Dynamics , vol.21
  • 175
    • 67649374569 scopus 로고    scopus 로고
    • Theme issue on "Time-reversible symmetry in dynamical systems". Phys. D 112 (1998)
    • (1998) Phys. D , vol.112
  • 176
    • 0031238062 scopus 로고    scopus 로고
    • Pseudospectra of linear operators
    • Trefethen L.N. Pseudospectra of linear operators. SIAM Rev. 39 (1997) 383-406
    • (1997) SIAM Rev. , vol.39 , pp. 383-406
    • Trefethen, L.N.1
  • 177
    • 45449123944 scopus 로고
    • Singular perturbation theory for traveling waves in excitable media (a review)
    • Tyson J.J., and Keener J.P. Singular perturbation theory for traveling waves in excitable media (a review). Phys. D 32 (1988) 327-361
    • (1988) Phys. D , vol.32 , pp. 327-361
    • Tyson, J.J.1    Keener, J.P.2
  • 178
    • 44049115047 scopus 로고
    • Fronts pulses, sources, and sinks in the generalized complex Ginzburg-Landau equation
    • Saarloos W.v., and Hohenberg P. Fronts pulses, sources, and sinks in the generalized complex Ginzburg-Landau equation. Phys. D 56 (1992) 303-367
    • (1992) Phys. D , vol.56 , pp. 303-367
    • Saarloos, W.v.1    Hohenberg, P.2
  • 179
    • 0033479139 scopus 로고    scopus 로고
    • Diffusive stability of rolls in the two-dimensional real and complex Swift-Hohenberg equation
    • Uecker H. Diffusive stability of rolls in the two-dimensional real and complex Swift-Hohenberg equation. Comm. Partial Differential Equations 24 (1999) 2109-2146
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 2109-2146
    • Uecker, H.1
  • 180
    • 0042834047 scopus 로고    scopus 로고
    • Stable modulating multi-pulse solutions for dissipative systems with a resonant spatially periodic forcing
    • Uecker H. Stable modulating multi-pulse solutions for dissipative systems with a resonant spatially periodic forcing. J. Nonlinear Sci. 11 (2001) 89-121
    • (2001) J. Nonlinear Sci. , vol.11 , pp. 89-121
    • Uecker, H.1
  • 182
    • 0000034625 scopus 로고
    • Homoclinic period blow-up in reversible and conservative systems
    • Vanderbauwhede A., and Fiedler B. Homoclinic period blow-up in reversible and conservative systems. Z. Angew. Math. Phys. 43 (1992) 292-318
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 292-318
    • Vanderbauwhede, A.1    Fiedler, B.2
  • 183
    • 0001412911 scopus 로고
    • Traveling Waves Solutions of Parabolic Systems
    • Amer. Math. Soc., Providence, RI
    • Volpert A.I., Volpert V.A., and Volpert V.A. Traveling Waves Solutions of Parabolic Systems. Transi. Math. Monographs Vol. 140 (1994), Amer. Math. Soc., Providence, RI
    • (1994) Transi. Math. Monographs , vol.140
    • Volpert, A.I.1    Volpert, V.A.2    Volpert, V.A.3
  • 184
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • Weinstein M.I. Modulational stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 16 (1985) 472-491
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 472-491
    • Weinstein, M.I.1
  • 185
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • Xin J. Front propagation in heterogeneous media. SIAM Rev. 42 (2000) 161-230
    • (2000) SIAM Rev. , vol.42 , pp. 161-230
    • Xin, J.1
  • 186
    • 0021853023 scopus 로고
    • Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
    • Yanagida E. Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations. J. Math. Biol-ogy 22 (1985) 81-104
    • (1985) J. Math. Biol-ogy , vol.22 , pp. 81-104
    • Yanagida, E.1
  • 187
    • 0002422398 scopus 로고
    • Branching of double pulse solutions from single pulse solutions in nerve axon equations
    • Yanagida E. Branching of double pulse solutions from single pulse solutions in nerve axon equations. J. Differential Equations 66 (1987) 243-262
    • (1987) J. Differential Equations , vol.66 , pp. 243-262
    • Yanagida, E.1
  • 188
    • 0039839578 scopus 로고
    • Stability of double-pulse solutions in nerve axon equations
    • Yanagida E., and Maginu K. Stability of double-pulse solutions in nerve axon equations. SIAM J. Appl. Math. 49 (1989) 1158-1173
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1158-1173
    • Yanagida, E.1    Maginu, K.2
  • 189
    • 0010765318 scopus 로고    scopus 로고
    • Multipulses of nonlinearly-coupled Schrödinger equations
    • Yew A.C. Multipulses of nonlinearly-coupled Schrödinger equations. J. Differential Equations 173 (2001) 92-137
    • (2001) J. Differential Equations , vol.173 , pp. 92-137
    • Yew, A.C.1
  • 190
    • 0004158480 scopus 로고    scopus 로고
    • Stability analysis of multipulses in nonlinearly-coupled Schrödinger equations
    • Yew A.C. Stability analysis of multipulses in nonlinearly-coupled Schrödinger equations. Indiana Univ. Math. J. 49 (2000) 1079-1124
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1079-1124
    • Yew, A.C.1
  • 191
    • 0004060909 scopus 로고    scopus 로고
    • Instability of multiple pulses in coupled nonlinear Schrödinger equations
    • Yew A.C., Sandstede B., and Jones C.K.R.T. Instability of multiple pulses in coupled nonlinear Schrödinger equations. Phys. Rev. E 61 (2000) 5886-5892
    • (2000) Phys. Rev. E , vol.61 , pp. 5886-5892
    • Yew, A.C.1    Sandstede, B.2    Jones, C.K.R.T.3
  • 193
    • 0009378734 scopus 로고    scopus 로고
    • Pointwise semigroup methods and stability of viscous shock waves
    • Zumbrun K., and Howard P. Pointwise semigroup methods and stability of viscous shock waves. Indiana Univ. Math. J. 47 (1999) 741-872
    • (1999) Indiana Univ. Math. J. , vol.47 , pp. 741-872
    • Zumbrun, K.1    Howard, P.2


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