메뉴 건너뛰기




Volumn 99, Issue 4, 1997, Pages 311-375

Convective linear stability of solitary waves for Boussinesq equations

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; KORTEWEG-DE VRIES EQUATION; LINEARIZATION; LYAPUNOV METHODS; NONLINEAR EQUATIONS; WATER WAVES;

EID: 0039573710     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.00063     Document Type: Article
Times cited : (48)

References (67)
  • 1
    • 0001681902 scopus 로고
    • Théorie de l'intumescence liquide, applelée onde solitaire ou de translation, se propageant dans un canal rectangulaire
    • M. J. BOUSSINESQ, Théorie de l'intumescence liquide, applelée onde solitaire ou de translation, se propageant dans un canal rectangulaire, C. R. Acad. Sci. Paris 72:755-759 (1871).
    • (1871) C. R. Acad. Sci. Paris , vol.72 , pp. 755-759
    • Boussinesq, M.J.1
  • 2
    • 0000982065 scopus 로고
    • Théorie générale des mouvements qui sont propagés dans un canal rectangulaire horizontal
    • M. J. BOUSSINESQ. Théorie générale des mouvements qui sont propagés dans un canal rectangulaire horizontal, C. R. Acad. Sci. Paris 73:256-260 (1871).
    • (1871) C. R. Acad. Sci. Paris , vol.73 , pp. 256-260
    • Boussinesq, M.J.1
  • 3
    • 0001864672 scopus 로고
    • Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond
    • M. J. BOUSSINESQ, Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl. 17:55-108 (1872).
    • (1872) J. Math. Pures Appl. , vol.17 , pp. 55-108
    • Boussinesq, M.J.1
  • 7
    • 0000339396 scopus 로고
    • On the theory of oscillatory waves
    • Johnson Reprint Corp., New York. (See Section 5.)
    • G. STOKES, On the theory of oscillatory waves, (1847). In Mathematical and Physical Papers, Johnson Reprint Corp., New York. (See Section 5.)
    • (1847) Mathematical and Physical Papers
    • Stokes, G.1
  • 9
    • 84990616652 scopus 로고
    • Inverse scattering and the Boussinesq equation
    • P. DEIFT, C. TOMEI, and E. TRUBOWITZ, Inverse scattering and the Boussinesq equation, Comm. Pure Appl. Math. 35:567-628 (1982).
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 567-628
    • Deift, P.1    Tomei, C.2    Trubowitz, E.3
  • 10
    • 0000060151 scopus 로고
    • On the stochastization of one dimensional chains of nonlinear oscillators
    • V. E. ZAKHAROV, On the stochastization of one dimensional chains of nonlinear oscillators, Soviet Phys. JETP 38:108-110 (1974).
    • (1974) Soviet Phys. JETP , vol.38 , pp. 108-110
    • Zakharov, V.E.1
  • 11
    • 33745586256 scopus 로고
    • Blow-up in the Boussinesq equation
    • S. K. TURITSYN, Blow-up in the Boussinesq equation, Phys. Rev. E 47:R796-799 (1993).
    • (1993) Phys. Rev. E , vol.47
    • Turitsyn, S.K.1
  • 13
    • 25344474267 scopus 로고
    • Dynamics of dense lattices
    • P. ROSENAU, Dynamics of dense lattices, Phys. Rev. B 36:5868-5876 (1987).
    • (1987) Phys. Rev. B , vol.36 , pp. 5868-5876
    • Rosenau, P.1
  • 14
    • 84958444374 scopus 로고
    • Calculations of the development of an undular bore
    • D. H. PEREGRINE, Calculations of the development of an undular bore, J. Fluid Mech. 25:321-330 (1966).
    • (1966) J. Fluid Mech. , vol.25 , pp. 321-330
    • Peregrine, D.H.1
  • 15
    • 0001681687 scopus 로고
    • Existence of solutions for the Boussinesq system of equations
    • M. SCHONBEK, Existence of solutions for the Boussinesq system of equations, J. Differential Equations 42:325-352 (1981).
    • (1981) J. Differential Equations , vol.42 , pp. 325-352
    • Schonbek, M.1
  • 16
    • 0001274115 scopus 로고
    • Regularity and uniqueness of solutions to the Boussinesq system of equations
    • C. AMICK, Regularity and uniqueness of solutions to the Boussinesq system of equations, J. Differential Equations 54:231-247 (1984).
    • (1984) J. Differential Equations , vol.54 , pp. 231-247
    • Amick, C.1
  • 17
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • R. L. PEGO and M. I. WEINSTEIN, Asymptotic stability of solitary waves, Comm. Math. Phys. 164:305-349 (1994).
    • (1994) Comm. Math. Phys. , vol.164 , pp. 305-349
    • Pego, R.L.1    Weinstein, M.I.2
  • 20
    • 0000058126 scopus 로고
    • Application of the method of spectral deformation to the Vlasov Poisson system
    • J. D. CRAWFORD and P. D. HISLOP, Application of the method of spectral deformation to the Vlasov Poisson system, Ann. Physics 189:265-317 (1989).
    • (1989) Ann. Physics , vol.189 , pp. 265-317
    • Crawford, J.D.1    Hislop, P.D.2
  • 21
    • 0013348022 scopus 로고
    • Application of the method of spectral deformation to the Vlasov Poisson system. II. Mathematical results
    • J. D. CRAWFORD and P. D. HISLOP, Application of the method of spectral deformation to the Vlasov Poisson system. II. Mathematical results, J. Math. Phys. 30:2819-2837 (1989).
    • (1989) J. Math. Phys. , vol.30 , pp. 2819-2837
    • Crawford, J.D.1    Hislop, P.D.2
  • 22
    • 4243765520 scopus 로고
    • Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping
    • S. H. STROGATZ, R. E. MIROLLO, anc P. C. MATTHEWS, Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping, Phys. Rev. Lett. 68(18):2730-2733 (1992).
    • (1992) Phys. Rev. Lett. , vol.68 , Issue.18 , pp. 2730-2733
    • Strogatz, S.H.1    Mirollo, R.E.2    Matthews, P.C.3
  • 23
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of traveling waves
    • J. ALEXANDER, R. GARDNER, and C. K. R. T. JONES, A topological invariant arising in the stability analysis of traveling waves, J. Reine Angew. Math. 410:167-212 (1990).
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.K.R.T.3
  • 24
    • 0016578299 scopus 로고
    • Nerve axon equations. IV. The stable and unstable impulse
    • J. W. EVANS, Nerve axon equations. IV. The stable and unstable impulse, Indiana Univ. Math. J. 24:1169-1190 (1975).
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.W.1
  • 25
    • 84870910659 scopus 로고
    • Spectral theory for contraction semigroups on Hilbert space
    • L. GEARHART, Spectral theory for contraction semigroups on Hilbert space, Trans. Amer. Math. Soc. 236:385-394 (1978).
    • (1978) Trans. Amer. Math. Soc. , vol.236 , pp. 385-394
    • Gearhart, L.1
  • 27
    • 0000374811 scopus 로고
    • Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces
    • F. HUANG, Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Differential Equations 1:43-56 (1985).
    • (1985) Ann. Differential Equations , vol.1 , pp. 43-56
    • Huang, F.1
  • 29
    • 0030558727 scopus 로고    scopus 로고
    • Asymptotic stability of solitary waves for the regularized long wave equation
    • J. R. MILLER and M. I. WEINSTEIN, Asymptotic stability of solitary waves for the regularized long wave equation, Comm. Pure Appl. Math. 49:399-441 (1996).
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 399-441
    • Miller, J.R.1    Weinstein, M.I.2
  • 31
    • 0039936117 scopus 로고
    • Multichannel nonlinear scattering theory for nonintegrable equations
    • Integrable Systems and Applications (M. Balabane, P. Lochak, and C. Sulem, Eds.), Springer, New York
    • A. SOFFER and M. I. WEINSTEIN, Multichannel nonlinear scattering theory for nonintegrable equations. In Integrable Systems and Applications (M. Balabane, P. Lochak, and C. Sulem, Eds.), Lecture Notes in Physics, Vol. 342, pp. 312-327, Springer, New York, 1988.
    • (1988) Lecture Notes in Physics , vol.342 , pp. 312-327
    • Soffer, A.1    Weinstein, M.I.2
  • 32
    • 0000301325 scopus 로고
    • Multichannel nonlinear scattering theory for nonintegrable equations
    • A. SOFFER and M. I. WEINSTEIN, Multichannel nonlinear scattering theory for nonintegrable equations, Comm. Math. Phys. 133:119-146 (1990).
    • (1990) Comm. Math. Phys. , vol.133 , pp. 119-146
    • Soffer, A.1    Weinstein, M.I.2
  • 33
    • 0001641727 scopus 로고
    • Multichannel nonlinear scattering theory for nonintegrable equations. II. The case of anisotropic potentials and data
    • A. SOFFER and M. I. WEINSTEIN, Multichannel nonlinear scattering theory for nonintegrable equations. II. The case of anisotropic potentials and data, J. Differential Equations 98:376-390 (1992).
    • (1992) J. Differential Equations , vol.98 , pp. 376-390
    • Soffer, A.1    Weinstein, M.I.2
  • 34
    • 0001265326 scopus 로고
    • Solitary waves and homoclinic orbits
    • N. J. BALMFORTH, Solitary waves and homoclinic orbits, Ann. Rev. Fluid Mech. 27:335-373 (1995).
    • (1995) Ann. Rev. Fluid Mech. , vol.27 , pp. 335-373
    • Balmforth, N.J.1
  • 35
    • 0004185917 scopus 로고
    • Wave evolution on a falling film
    • H.-C. CHANG, Wave evolution on a falling film, Ann. Rev. Fluid Mech. 26:103-136 (1994).
    • (1994) Ann. Rev. Fluid Mech. , vol.26 , pp. 103-136
    • Chang, H.-C.1
  • 36
    • 0000128696 scopus 로고    scopus 로고
    • Local stability theory of solitary pulses in an active medium
    • H.-C. CHANG, E. A. DEMEKHIN, and D I. KOPELEVICH, Local stability theory of solitary pulses in an active medium, Phys. D, 97:353-375 (1996).
    • (1996) Phys. D , vol.97 , pp. 353-375
    • Chang, H.-C.1    Demekhin, E.A.2    Kopelevich, D.I.3
  • 37
    • 0031119008 scopus 로고    scopus 로고
    • On the spectra of pulses in a nearly integrable system
    • T. OGAWA and H. SUZUKI, On the spectra of pulses in a nearly integrable system, SIAM J. Appl. 57:485-500 (1997).
    • (1997) SIAM J. Appl. , vol.57 , pp. 485-500
    • Ogawa, T.1    Suzuki, H.2
  • 40
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry, I
    • M. GRILLAKIS, J. SHATAH, and W. STRAUSS, Stability theory of solitary waves in the presence of symmetry, I, J. Funct. Anal. 74:160-197 (1988).
    • (1988) J. Funct. Anal. , vol.74 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 41
    • 0011418598 scopus 로고
    • Stability theory for solitary wave solutions of scalar field equations
    • D. B. HENRY, J. F. PEREZ, and W. F. WRESZINSKI, Stability theory for solitary wave solutions of scalar field equations, Commun. Math. Phys. 85:351-361 (1982).
    • (1982) Commun. Math. Phys. , vol.85 , pp. 351-361
    • Henry, D.B.1    Perez, J.F.2    Wreszinski, W.F.3
  • 42
    • 84976048247 scopus 로고
    • Stability theorem for KdV type equations
    • E. W. LAEDKE and K. H. SPATSCHEK, Stability theorem for KdV type equations, J. Plasma Phys. 32:263-272 (1984).
    • (1984) J. Plasma Phys. , vol.32 , pp. 263-272
    • Laedke, E.W.1    Spatschek, K.H.2
  • 43
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • M. I. WEINSTEIN, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16:472-491 (1985).
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 472-491
    • Weinstein, M.I.1
  • 44
    • 0040170304 scopus 로고
    • On the solitary traveling wave of the generalized Korteweg-de Vries equation
    • Nonlinear Systems of Partial Differential Equations in Applied Mathematics (B. Nicolaenko, D. Holm, and J. Hyman, Eds.), Amer. Math. Soc., Providence
    • M. I. WEINSTEIN, On the solitary traveling wave of the generalized Korteweg-de Vries equation. In Nonlinear Systems of Partial Differential Equations in Applied Mathematics (B. Nicolaenko, D. Holm, and J. Hyman, Eds.), Lectures in Appl. Math., Vol. 23, Part 2, Amer. Math. Soc., Providence, 1986.
    • (1986) Lectures in Appl. Math. , vol.23 , Issue.2 PART
    • Weinstein, M.I.1
  • 45
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • M. I. WEINSTEIN, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39:51-68 (1986).
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 51-68
    • Weinstein, M.I.1
  • 46
    • 84946267644 scopus 로고
    • Existence and dynamical stability theory of solitary wave solutions of equations governing long wave propagation
    • M. I. WEINSTEIN, Existence and dynamical stability theory of solitary wave solutions of equations governing long wave propagation, Comm. Partial Differential Equations 12:1133-1173 (1987).
    • (1987) Comm. Partial Differential Equations , vol.12 , pp. 1133-1173
    • Weinstein, M.I.1
  • 47
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • T. CAZENAVE and P.-L. LIONS, Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys. 85:549-561 (1982).
    • (1982) Commun. Math. Phys. , vol.85 , pp. 549-561
    • Cazenave, T.1    Lions, P.-L.2
  • 48
    • 0001687530 scopus 로고
    • Conditions for nonlinear stability of stationary curvilinear flows of an ideal fluid
    • V. I. ARNOL'D, Conditions for nonlinear stability of stationary curvilinear flows of an ideal fluid, Dokl. Mat. Nauk. 162:773-777 (1965).
    • (1965) Dokl. Mat. Nauk. , vol.162 , pp. 773-777
    • Arnol'd, V.I.1
  • 49
    • 0002245635 scopus 로고
    • Nonlinear stability of fluid and plasma equilibria
    • D. D. HOLM, J. E. MARSDEN, T. RATIU, and A. WEINSTEIN, Nonlinear stability of fluid and plasma equilibria, Phys. Rep. 123:1-116 (1985).
    • (1985) Phys. Rep. , vol.123 , pp. 1-116
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.3    Weinstein, A.4
  • 50
    • 36849120778 scopus 로고
    • On the stability of plasma in static equilibrium
    • M. D. KRUSKAL and C. R. OBERMAN, On the stability of plasma in static equilibrium, Phys. Fluids 1:275-280 (1958).
    • (1958) Phys. Fluids , vol.1 , pp. 275-280
    • Kruskal, M.D.1    Oberman, C.R.2
  • 51
    • 0039578847 scopus 로고
    • A remark on the solitary wave stability for a Boussinesq equation
    • L. Debnath, Ed., World Scientific, Singapore
    • P. SMEREKA, A remark on the solitary wave stability for a Boussinesq equation. In Nonlinear Dispersive Wave Systems (L. Debnath, Ed.), pp. 255-263, World Scientific, Singapore, 1992.
    • (1992) Nonlinear Dispersive Wave Systems , pp. 255-263
    • Smereka, P.1
  • 52
    • 0001726136 scopus 로고
    • Oscillatory instability of solitary waves in a continuum model of lattice vibrations
    • R. L. PEGO, P. SMEREKA, and M. I. WEINSTEIN, Oscillatory instability of solitary waves in a continuum model of lattice vibrations, Nonlinearity 8:921-941 (1995).
    • (1995) Nonlinearity , vol.8 , pp. 921-941
    • Pego, R.L.1    Smereka, P.2    Weinstein, M.I.3
  • 53
    • 0003147442 scopus 로고
    • The existence of internal solitary waves in a two-fluid system near the KdV limit
    • J. L. BONA and R. SACHS, The existence of internal solitary waves in a two-fluid system near the KdV limit, Geophys. Astrophys. Fluid Dynamics 48:25-51 (1989).
    • (1989) Geophys. Astrophys. Fluid Dynamics , vol.48 , pp. 25-51
    • Bona, J.L.1    Sachs, R.2
  • 54
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves
    • D. J. KORTEWEG and G. DE VRIES, On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves, Philos. Mag. (5) 39:422-443 (1895).
    • (1895) Philos. Mag. (5) , vol.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 55
    • 0000133747 scopus 로고
    • On the stability of solitary waves
    • J. L. BONA, On the stability of solitary waves, Proc. Roy. Soc. London Ser. A 344:363-374 (1975).
    • (1975) Proc. Roy. Soc. London Ser. A , vol.344 , pp. 363-374
    • Bona, J.L.1
  • 56
    • 0019559935 scopus 로고
    • The Korteweg-de Vries equation: A historical essay
    • J. W. MILES, The Korteweg-de Vries equation: A historical essay, J. Fluid Mech. 106:131-147 (1981).
    • (1981) J. Fluid Mech. , vol.106 , pp. 131-147
    • Miles, J.W.1
  • 58
    • 36749107088 scopus 로고
    • Stability of solitary waves in shallow water
    • J. G. BERRYMAN, Stability of solitary waves in shallow water, Phys. Fluids 19:771-777 (1976).
    • (1976) Phys. Fluids , vol.19 , pp. 771-777
    • Berryman, J.G.1
  • 59
    • 0015419996 scopus 로고
    • Weakly nonlinear dispersive waves: A discussion centered about the Korteweg-de Vries equation
    • A. JEFFREY and T. KAKUTANI, Weakly nonlinear dispersive waves: A discussion centered about the Korteweg-de Vries equation, SIAM Rev. 14:582-643 (1972).
    • (1972) SIAM Rev. , vol.14 , pp. 582-643
    • Jeffrey, A.1    Kakutani, T.2
  • 61
    • 84967743294 scopus 로고
    • Stability of the traveling wave solution to the FitzHugh-Hagumo equation
    • C. K. R. T. JONES, Stability of the traveling wave solution to the FitzHugh-Hagumo equation. Trans. Amer. Math. Soc. 286:431-469 (1984).
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.K.R.T.1
  • 63
    • 77956868212 scopus 로고
    • Evans' function, Melnikov's integral and solitary wave instabilities
    • W. F. Ames, J. V. Herod, and E. M. Harrell, Eds., Academic Press, Orlando
    • R. L. PEGO and M. I. WEINSTEIN, Evans' function, Melnikov's integral and solitary wave instabilities. In Differential Equations with Applications to Mathematical Physics (W. F. Ames, J. V. Herod, and E. M. Harrell, Eds.), pp. 273-286, Academic Press, Orlando, 1993.
    • (1993) Differential Equations with Applications to Mathematical Physics , pp. 273-286
    • Pego, R.L.1    Weinstein, M.I.2
  • 64
    • 0003401596 scopus 로고
    • Introduction to the theory of linear nonselfadjoint operators
    • Amer. Math. Soc., Providence
    • I. C. GOHBERG and M. G. KREIN, Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monog., Vol. 18, Amer. Math. Soc., Providence, 1969.
    • (1969) Transl. Math. Monog. , vol.18
    • Gohberg, I.C.1    Krein, M.G.2
  • 65
    • 84968509293 scopus 로고
    • 2 and the Fourier transform
    • 2 and the Fourier transform, Proc. Amer. Math. Soc. 95:252-254 (1985).
    • (1985) Proc. Amer. Math. Soc. , vol.95 , pp. 252-254
    • Pego, R.L.1
  • 67
    • 0002709196 scopus 로고
    • Dichotomies in stability theory
    • Springer-Verlag, New York
    • W. A. COPPEL, Dichotomies in Stability Theory, Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, New York, 1978.
    • (1978) Lecture Notes in Mathematics , vol.629
    • Coppel, W.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.