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Volumn 2, Issue , 2002, Pages 759-834

Chapter 15 The Ginzburg-Landau equation in its role as a modulation equation

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EID: 67649370945     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80036-4     Document Type: Chapter
Times cited : (130)

References (152)
  • 1
    • 38249020894 scopus 로고
    • Existence and finite dimensionality of the global attractor for evolution equations on un-bounded domains
    • Abergel F. Existence and finite dimensionality of the global attractor for evolution equations on un-bounded domains. J. Differential Equations 83 (1990) 85-108
    • (1990) J. Differential Equations , vol.83 , pp. 85-108
    • Abergel, F.1
  • 2
    • 21844484628 scopus 로고
    • Bifurcations of Poiseuille flow between parallel plates: three-dimensional solutions with large spanwise wavelength
    • Afendikov A.L., and Mielke A. Bifurcations of Poiseuille flow between parallel plates: three-dimensional solutions with large spanwise wavelength. Arch. Rat. Mech. Anal. 129 (1995) 101-127
    • (1995) Arch. Rat. Mech. Anal. , vol.129 , pp. 101-127
    • Afendikov, A.L.1    Mielke, A.2
  • 3
    • 0033544737 scopus 로고    scopus 로고
    • Bifurcation of homoclinic orbits to a saddle-focus in reversible systems with SO(2)-symmetry
    • Afendikov A.L., and Mielke A. Bifurcation of homoclinic orbits to a saddle-focus in reversible systems with SO(2)-symmetry. J. Differential Equations 159 (1999) 370-402
    • (1999) J. Differential Equations , vol.159 , pp. 370-402
    • Afendikov, A.L.1    Mielke, A.2
  • 4
    • 0035530955 scopus 로고    scopus 로고
    • Multi-pulse solutions to the Navier-Stokes problem between parallel plates
    • Afendikov A.L., and Mielke A. Multi-pulse solutions to the Navier-Stokes problem between parallel plates. Zeits. Angew. Math. Physik (ZAMP) 52 (2001) 79-100
    • (2001) Zeits. Angew. Math. Physik (ZAMP) , vol.52 , pp. 79-100
    • Afendikov, A.L.1    Mielke, A.2
  • 5
    • 67649330346 scopus 로고    scopus 로고
    • Nonlocal modulation equations for viscous fluid layer problems and persis-tence of spatially localized perturbations
    • (submitted)
    • (submitted). Afendikov A.L., and Mielke A. Nonlocal modulation equations for viscous fluid layer problems and persis-tence of spatially localized perturbations. Zeits. Angew. Math. Mech (ZAMM) Suppl. (2000)
    • (2000) Zeits. Angew. Math. Mech (ZAMM) Suppl.
    • Afendikov, A.L.1    Mielke, A.2
  • 6
    • 67649328072 scopus 로고    scopus 로고
    • Symmetry and chaos in the complex Ginzburg-Landau equation. I: reflectional symmetries
    • (to appear)
    • (to appear). Aston P.J., and Laing C.R. Symmetry and chaos in the complex Ginzburg-Landau equation. I: reflectional symmetries. Dynamics Stabil. Systems (1998)
    • (1998) Dynamics Stabil. Systems
    • Aston, P.J.1    Laing, C.R.2
  • 7
    • 67649334069 scopus 로고    scopus 로고
    • II: translational symmetries
    • (to appear)
    • (to appear). II: translational symmetries. Phys. D (1999)
    • (1999) Phys. D
  • 8
    • 84972273463 scopus 로고
    • Attractors of partial differential equations in an unbounded domain
    • Babin A.V., and Vishik M.I. Attractors of partial differential equations in an unbounded domain. Proc. Roy. Soc. Edinburgh Ser. A 116 (1990) 221-243
    • (1990) Proc. Roy. Soc. Edinburgh Ser. A , vol.116 , pp. 221-243
    • Babin, A.V.1    Vishik, M.I.2
  • 10
    • 0000922548 scopus 로고
    • On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation
    • Bartucelli M.V., Constantin P., Doering C.R., Gibbon J.D., and Gisselfält M. On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation. Phys. D 44 (1990) 412-444
    • (1990) Phys. D , vol.44 , pp. 412-444
    • Bartucelli, M.V.1    Constantin, P.2    Doering, C.R.3    Gibbon, J.D.4    Gisselfält, M.5
  • 11
    • 22244466122 scopus 로고    scopus 로고
    • Length scales in solutions of the complex Ginzburg-Landau equation
    • Bartucelli M.V., Gibbon J.D., and Oliver M. Length scales in solutions of the complex Ginzburg-Landau equation. Phys. D 89 (1996) 267-286
    • (1996) Phys. D , vol.89 , pp. 267-286
    • Bartucelli, M.V.1    Gibbon, J.D.2    Oliver, M.3
  • 12
    • 67649338654 scopus 로고    scopus 로고
    • Inviscid limits of the complex Ginzburg-Landau equation
    • May, Université de Nice
    • May. Bechouche P., and Jüngel A. Inviscid limits of the complex Ginzburg-Landau equation. Prépubl. No. 545 (1999), Université de Nice
    • (1999) Prépubl. No. 545
    • Bechouche, P.1    Jüngel, A.2
  • 13
    • 0003001381 scopus 로고
    • Formation of spatial patterns and holes in the generalised Ginzburg-Landau equation
    • Bekki N., and Nozakki B. Formation of spatial patterns and holes in the generalised Ginzburg-Landau equation. Phys. Lett. A 110 (1985) 133-135
    • (1985) Phys. Lett. A , vol.110 , pp. 133-135
    • Bekki, N.1    Nozakki, B.2
  • 14
    • 84974324325 scopus 로고
    • Finite amplitude convection between stress-free boundaries; Ginzburg-Landau equations and modulation theory
    • Bernoff A.J. Finite amplitude convection between stress-free boundaries; Ginzburg-Landau equations and modulation theory. European J. Appl. Math. 5 (1994) 267-282
    • (1994) European J. Appl. Math. , vol.5 , pp. 267-282
    • Bernoff, A.J.1
  • 16
    • 67649314724 scopus 로고    scopus 로고
    • A continuation framework for invariant subspaces and its applica-tion to traveling waves
    • (to appear). Hamburg-Harburg T.U., Mackens W., Voß H., and Keil F. (Eds)
    • (to appear). Beyn W.-J., Kleßand W., and Thümmler V. A continuation framework for invariant subspaces and its applica-tion to traveling waves. In: Hamburg-Harburg T.U., Mackens W., Voß H., and Keil F. (Eds). Proc. of the Conference SCC II (1999)
    • (1999) Proc. of the Conference SCC II
    • Beyn, W.-J.1    Kleßand, W.2    Thümmler, V.3
  • 19
    • 0003791296 scopus 로고    scopus 로고
    • On the theory of validity of amplitude equations
    • Utrecht University
    • Bollerman P. On the theory of validity of amplitude equations. Ph.D. Thesis (1996), Utrecht University
    • (1996) Ph.D. Thesis
    • Bollerman, P.1
  • 20
    • 0002339568 scopus 로고
    • On the justification of the Ginzburg-Landau approximation
    • Nonlinear Dynamics and Pattern Formation in Natural Environment. Doelman A., and Harten A.v. (Eds), Longman, Harlow
    • Bollerman P., Schneider G., and Harten A.v. On the justification of the Ginzburg-Landau approximation. In: Doelman A., and Harten A.v. (Eds). Nonlinear Dynamics and Pattern Formation in Natural Environment. Pitman Res. Notes Vol. 335 (1995), Longman, Harlow 20-36
    • (1995) Pitman Res. Notes , vol.335 , pp. 20-36
    • Bollerman, P.1    Schneider, G.2    Harten, A.v.3
  • 21
    • 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
  • 22
    • 0039959277 scopus 로고
    • Instability of spatially quasi-periodic states of the Ginzburg-Landau equa-tion
    • Bridges T.J., and Rowlands G. Instability of spatially quasi-periodic states of the Ginzburg-Landau equa-tion. Proc. Roy. Soc. London Ser. A 444 (1994) 347-362
    • (1994) Proc. Roy. Soc. London Ser. A , vol.444 , pp. 347-362
    • Bridges, T.J.1    Rowlands, G.2
  • 23
    • 3042951460 scopus 로고    scopus 로고
    • Torsion numbers, a tool for the examination of symmetric reaction-diffusion systems related to oscillation numbers
    • Büger M. Torsion numbers, a tool for the examination of symmetric reaction-diffusion systems related to oscillation numbers. Discrete Cont. Dynam. Systems 4 (1998) 691-708
    • (1998) Discrete Cont. Dynam. Systems , vol.4 , pp. 691-708
    • Büger, M.1
  • 24
    • 0000067561 scopus 로고
    • Macroscopic models for superconductivity
    • Chapman S.J., Howison S.D., and Ockendon J.R. Macroscopic models for superconductivity. SIAM Rev. 34 (1992) 529-560
    • (1992) SIAM Rev. , vol.34 , pp. 529-560
    • Chapman, S.J.1    Howison, S.D.2    Ockendon, J.R.3
  • 26
    • 0002723604 scopus 로고
    • Thermodynamic limit of the Ginzburg-Landau equations
    • Collet P. Thermodynamic limit of the Ginzburg-Landau equations. Nonlinearity 7 (1994) 1175-1190
    • (1994) Nonlinearity , vol.7 , pp. 1175-1190
    • Collet, P.1
  • 27
    • 0000484304 scopus 로고
    • The time-dependent amplitude equation for the Swift-Hohenberg problem
    • Collet P., and Eckmann J.-P. The time-dependent amplitude equation for the Swift-Hohenberg problem. Comm. Math. Phys. 132 (1990) 139-153
    • (1990) Comm. Math. Phys. , vol.132 , pp. 139-153
    • Collet, P.1    Eckmann, J.-P.2
  • 28
    • 0040359126 scopus 로고
    • Solutions without phase-slip for the Ginsburg-Landau equation
    • Collet P., and Eckmann J.-P. Solutions without phase-slip for the Ginsburg-Landau equation. Comm. Math. Phys. 145 (1992) 345-356
    • (1992) Comm. Math. Phys. , vol.145 , pp. 345-356
    • Collet, P.1    Eckmann, J.-P.2
  • 29
    • 0033447899 scopus 로고    scopus 로고
    • Extensive properties of the complex Ginzburg-Landau equation
    • Collet P., and Eckmann J.-P. Extensive properties of the complex Ginzburg-Landau equation. Comm. Math. Phys. 200 (1999) 699-722
    • (1999) Comm. Math. Phys. , vol.200 , pp. 699-722
    • Collet, P.1    Eckmann, J.-P.2
  • 30
    • 0033130277 scopus 로고    scopus 로고
    • The definition and measurement of the topological entropy per unit volume in parabolic PDEs
    • Collet P., and Eckmann J.-P. The definition and measurement of the topological entropy per unit volume in parabolic PDEs. Nonlinearity 12 (1999) 451-473
    • (1999) Nonlinearity , vol.12 , pp. 451-473
    • Collet, P.1    Eckmann, J.-P.2
  • 31
    • 0040953231 scopus 로고
    • Diffusive repair for the Ginsburg-Landau equation
    • Collet P., Eckmann J.-P., and Epstein H. Diffusive repair for the Ginsburg-Landau equation. Helv. Phys. Acta 65 (1992) 56-92
    • (1992) Helv. Phys. Acta , vol.65 , pp. 56-92
    • Collet, P.1    Eckmann, J.-P.2    Epstein, H.3
  • 32
    • 0000784514 scopus 로고
    • Nonlinear modulation of gravity waves
    • Craig W., Sulem C., and Sulem P.L. Nonlinear modulation of gravity waves. Nonlinearity 5 (1992) 497-522
    • (1992) Nonlinearity , vol.5 , pp. 497-522
    • Craig, W.1    Sulem, C.2    Sulem, P.L.3
  • 33
    • 0347028241 scopus 로고
    • On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow
    • Davey A., Hocking L.M., and Stewartson K. On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 63 (1974) 529-536
    • (1974) J. Fluid Mech. , vol.63 , pp. 529-536
    • Davey, A.1    Hocking, L.M.2    Stewartson, K.3
  • 34
    • 0000061142 scopus 로고
    • Order parameter and amplitude equations for the Rayleigh-Bénard problem
    • Decker W., and Pesch W. Order parameter and amplitude equations for the Rayleigh-Bénard problem. J. Phys. II France 4 (1994) 419-438
    • (1994) J. Phys. II France , vol.4 , pp. 419-438
    • Decker, W.1    Pesch, W.2
  • 35
    • 67649304000 scopus 로고    scopus 로고
    • Deift P., Levermore C.D., and Wayne C.E. (Eds), Amer. Math. Soc., Providence, RI
    • In: Deift P., Levermore C.D., and Wayne C.E. (Eds). Dynamical Systems and Probabilistic Methods in Partial Differential Equations. Lecture Appl. Math. Vol. 31 (1996), Amer. Math. Soc., Providence, RI
    • (1996) Lecture Appl. Math. , vol.31
  • 36
    • 84959666786 scopus 로고
    • Nonlinear wavenumber interaction in near critical two-dimensional flows
    • DiPrima R.C., Eckhaus W., and Segel L. Nonlinear wavenumber interaction in near critical two-dimensional flows. J. Fluid Mech. 49 (1971) 705-744
    • (1971) J. Fluid Mech. , vol.49 , pp. 705-744
    • DiPrima, R.C.1    Eckhaus, W.2    Segel, L.3
  • 37
    • 51249170613 scopus 로고
    • Traveling waves in the complex Ginzburg-Landau equation
    • Doelman A. Traveling waves in the complex Ginzburg-Landau equation. J. Nonlinear Sci. 3 (1993) 225-266
    • (1993) J. Nonlinear Sci. , vol.3 , pp. 225-266
    • Doelman, A.1
  • 38
    • 22244440233 scopus 로고    scopus 로고
    • Breaking the hidden symmetry in the Ginzburg-Landau equation
    • Doelman A. Breaking the hidden symmetry in the Ginzburg-Landau equation. Phys. D 97 (1996) 398-428
    • (1996) Phys. D , vol.97 , pp. 398-428
    • Doelman, A.1
  • 39
    • 0000238802 scopus 로고
    • Periodic and quasi-periodic solutions of degenerate modulation equations
    • Doelman A., and Eckhaus W. Periodic and quasi-periodic solutions of degenerate modulation equations. Phys. D 53 (1991) 249-266
    • (1991) Phys. D , vol.53 , pp. 249-266
    • Doelman, A.1    Eckhaus, W.2
  • 40
  • 41
    • 0009268172 scopus 로고    scopus 로고
    • Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms
    • Doelman A., and Rottschäfer V. Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms. J. Nonlinear Sci. 7 (1997) 371-409
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 371-409
    • Doelman, A.1    Rottschäfer, V.2
  • 42
    • 0000287007 scopus 로고
    • Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation
    • Doelman A., and Titi E.S. Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation. Numer. Funct. Anal. Optim. 14 (1993) 299-321
    • (1993) Numer. Funct. Anal. Optim. , vol.14 , pp. 299-321
    • Doelman, A.1    Titi, E.S.2
  • 43
    • 67649304001 scopus 로고
    • Doelman A., and Harten A.v. (Eds), Longman, Harlow
    • In: Doelman A., and Harten A.v. (Eds). Nonlinear Dynamics and Pattern Formation in Natural Environment. Pitman Res. Notes Vol. 335 (1995), Longman, Harlow
    • (1995) Pitman Res. Notes , vol.335
  • 44
    • 0000967970 scopus 로고
    • Weak and strong solutions of the complex Ginzburg-Landau equation
    • Doering C.R., Gibbon J.D., and Levermore C.D. Weak and strong solutions of the complex Ginzburg-Landau equation. Phys. D 71 (1994) 285-318
    • (1994) Phys. D , vol.71 , pp. 285-318
    • Doering, C.R.1    Gibbon, J.D.2    Levermore, C.D.3
  • 45
    • 0000153785 scopus 로고
    • Low-dimensional behaviour in the complex Ginzburg-Landau equation
    • Doering C.R., Gibbon J.D., Holm D.D., and Nicolaenko B. Low-dimensional behaviour in the complex Ginzburg-Landau equation. Nonlinearity 1 (1988) 279-309
    • (1988) Nonlinearity , vol.1 , pp. 279-309
    • Doering, C.R.1    Gibbon, J.D.2    Holm, D.D.3    Nicolaenko, B.4
  • 46
    • 0026838281 scopus 로고
    • Analysis and approximation of the Ginzburg-Landau model of superconductivity
    • Du Q., Gunzburger M.D., and Peterson J.S. Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Rev. 34 (1992) 54-81
    • (1992) SIAM Rev. , vol.34 , pp. 54-81
    • Du, Q.1    Gunzburger, M.D.2    Peterson, J.S.3
  • 47
    • 0001024873 scopus 로고
    • Global existence for a generalized Ginzburg-Landau equation
    • Duan J., Titi E.S., and Holmes P. Global existence for a generalized Ginzburg-Landau equation. Nonlin-earity 5 (1992) 1303-1314
    • (1992) Nonlin-earity , vol.5 , pp. 1303-1314
    • Duan, J.1    Titi, E.S.2    Holmes, P.3
  • 48
    • 0000815546 scopus 로고
    • Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation
    • Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Nonlinearity 6 (1993) 915-933
    • (1993) Nonlinearity , vol.6 , pp. 915-933
  • 49
    • 0013455619 scopus 로고
    • Studies in Non-Linear Stability Theory
    • Springer, Berlin
    • Eckhaus W. Studies in Non-Linear Stability Theory. Springer Tracts in Nat. Philos. 6 (1965), Springer, Berlin
    • (1965) Springer Tracts in Nat. Philos. 6
    • Eckhaus, W.1
  • 50
    • 51249162531 scopus 로고
    • The Ginzburg-Landau manifold is an attractor
    • Eckhaus W. The Ginzburg-Landau manifold is an attractor. J. Nonlinear Sci. 3 (1993) 329-348
    • (1993) J. Nonlinear Sci. , vol.3 , pp. 329-348
    • Eckhaus, W.1
  • 51
    • 0000810343 scopus 로고
    • Strong selection or rejection of spatially periodic patterns in degenerate bifur-cations
    • Eckhaus W., and Iooss G. Strong selection or rejection of spatially periodic patterns in degenerate bifur-cations. Phys. D 39 (1989) 124-146
    • (1989) Phys. D , vol.39 , pp. 124-146
    • Eckhaus, W.1    Iooss, G.2
  • 52
    • 21144465106 scopus 로고
    • Front solutions for the Ginzburg-Landau equation
    • Eckmann J.-P., and Gallay T. Front solutions for the Ginzburg-Landau equation. Comm. Math. Phys. 152 (1993) 221-248
    • (1993) Comm. Math. Phys. , vol.152 , pp. 221-248
    • Eckmann, J.-P.1    Gallay, T.2
  • 53
    • 2942736915 scopus 로고
    • Phase slips and the Eckhaus instability
    • Eckmann J.-P., Gallay T., and Wayne C.E. Phase slips and the Eckhaus instability. Nonlinearity 8 (1995) 943-961
    • (1995) Nonlinearity , vol.8 , pp. 943-961
    • Eckmann, J.-P.1    Gallay, T.2    Wayne, C.E.3
  • 54
    • 22444452272 scopus 로고    scopus 로고
    • Coarsening by Ginzburg-Landau dynamics
    • Eckmann J.-P., and Rougemont J. Coarsening by Ginzburg-Landau dynamics. Comm. Math. Phys. 199 (1999) 441-470
    • (1999) Comm. Math. Phys. , vol.199 , pp. 441-470
    • Eckmann, J.-P.1    Rougemont, J.2
  • 56
    • 0346960800 scopus 로고    scopus 로고
    • The attractor for a nonlinear reaction-diffusion system in an unbounded domain
    • WIAS, Berlin
    • Efendiev M., and Zelik S. The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Preprint No. 505 (1999), WIAS, Berlin
    • (1999) Preprint No. 505
    • Efendiev, M.1    Zelik, S.2
  • 58
    • 0038938431 scopus 로고    scopus 로고
    • Self-focusing in the complex Ginzburg-Landau equation limit of the critical non-linear Schrödinger equation
    • Preprint Tel Aviv University. (submitted) (submitted)
    • Preprint Tel Aviv University. Fibich G., and Levy D. Self-focusing in the complex Ginzburg-Landau equation limit of the critical non-linear Schrödinger equation. (submitted). Phys. Lett. A (1998) (submitted)
    • (1998) Phys. Lett. A
    • Fibich, G.1    Levy, D.2
  • 59
    • 0007228109 scopus 로고
    • Periodic patterns and traveling fronts for the Ginzburg-Landau equation
    • Mielke A., and Kirchgässner K. (Eds), World Scientific, Singapore
    • Gallay T. Periodic patterns and traveling fronts for the Ginzburg-Landau equation. In: Mielke A., and Kirchgässner K. (Eds). Structure and Dy-namics of Nonlinear Waves in Fluids (1995), World Scientific, Singapore 230-238
    • (1995) Structure and Dy-namics of Nonlinear Waves in Fluids , pp. 230-238
    • Gallay, T.1
  • 60
    • 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
  • 62
    • 0000322045 scopus 로고
    • Dimension of the attractor associated to the Ginzburg-Landau partial differential equation
    • Ghidaglia J.-M., and Héron B. Dimension of the attractor associated to the Ginzburg-Landau partial differential equation. Phys. D 28 (1987) 282-304
    • (1987) Phys. D , vol.28 , pp. 282-304
    • Ghidaglia, J.-M.1    Héron, B.2
  • 63
    • 0001203317 scopus 로고    scopus 로고
    • The Cauchy problem in local spaces for the complex Ginzburg-Landau equation I. Compactness methods
    • Ginibre J., and Velo G. The Cauchy problem in local spaces for the complex Ginzburg-Landau equation I. Compactness methods. Phys. D 85 (1996) 191-228
    • (1996) Phys. D , vol.85 , pp. 191-228
    • Ginibre, J.1    Velo, G.2
  • 64
    • 0039768823 scopus 로고    scopus 로고
    • The Cauchy problem in local spaces for the complex Ginzburg-Landau equation II. Contraction methods
    • Ginibre J., and Velo G. The Cauchy problem in local spaces for the complex Ginzburg-Landau equation II. Contraction methods. Comm. Math. Phys. 187 (1997) 45-79
    • (1997) Comm. Math. Phys. , vol.187 , pp. 45-79
    • Ginibre, J.1    Velo, G.2
  • 66
    • 0001645343 scopus 로고
    • Spiral waves in reaction diffusion equations
    • Hagan P. 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.1
  • 67
    • 0003293929 scopus 로고
    • Asymptotic Behavior of Dissipative Systems
    • Amer. Math. Soc., Providence, RI
    • Hale J.K. Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs Vol. 25 (1988), Amer. Math. Soc., Providence, RI
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 68
    • 0011020485 scopus 로고
    • Limits of semigroups depending on parameters
    • Addendum in 1 (1994), 361
    • Addendum in 1 (1994), 361. Hale J.K., and Raugel G. Limits of semigroups depending on parameters. Resenhas (Univ. São Paulo) 1 (1993) 1-45
    • (1993) Resenhas (Univ. São Paulo) , vol.1 , pp. 1-45
    • Hale, J.K.1    Raugel, G.2
  • 70
    • 0033482571 scopus 로고    scopus 로고
    • Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
    • Haragus-Courcelle M., and Schneider G. Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zeits. Angew. Math. Physik (ZAMP) 50 (1999) 120-151
    • (1999) Zeits. Angew. Math. Physik (ZAMP) , vol.50 , pp. 120-151
    • Haragus-Courcelle, M.1    Schneider, G.2
  • 71
    • 0000547485 scopus 로고
    • Nonlinear modulation of gravitational waves
    • Hasimoto H., and Ono H. Nonlinear modulation of gravitational waves. J. Phys. Soc. Japan 33 (1972) 805-811
    • (1972) J. Phys. Soc. Japan , vol.33 , pp. 805-811
    • Hasimoto, H.1    Ono, H.2
  • 72
    • 0000273393 scopus 로고
    • On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance
    • Hocking L.M., and Stewartson K. On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance. Proc. Roy. Soc. London A 326 (1972) 289-313
    • (1972) Proc. Roy. Soc. London A , vol.326 , pp. 289-313
    • Hocking, L.M.1    Stewartson, K.2
  • 73
    • 0002436447 scopus 로고
    • Spatial structure of time periodic solutions of the Ginzburg-Landau equation
    • Holmes P. Spatial structure of time periodic solutions of the Ginzburg-Landau equation. Phys. D 23 (1986) 84-90
    • (1986) Phys. D , vol.23 , pp. 84-90
    • Holmes, P.1
  • 75
    • 34249918820 scopus 로고
    • Bifurcating time periodic solutions of Navier-Stokes equations in infinite cylin-ders
    • Iooss G., and Mielke A. Bifurcating time periodic solutions of Navier-Stokes equations in infinite cylin-ders. J. Nonlinear Sci. 1 (1991) 106-146
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 106-146
    • Iooss, G.1    Mielke, A.2
  • 76
    • 0007288360 scopus 로고
    • Time-periodic Ginzburg-Landau equations for one-dimensional patterns with large wave length
    • Iooss G., and Mielke A. Time-periodic Ginzburg-Landau equations for one-dimensional patterns with large wave length. Zeits. Angew. Math. Physik (ZAMP) 43 (1992) 125-138
    • (1992) Zeits. Angew. Math. Physik (ZAMP) , vol.43 , pp. 125-138
    • Iooss, G.1    Mielke, A.2
  • 77
    • 0000677116 scopus 로고
    • Theory of the steady Ginzburg-Landau equation in hydrodynamic stability problems
    • Iooss G., Mielke A., and Demay Y. Theory of the steady Ginzburg-Landau equation in hydrodynamic stability problems. Europ. J. Mech. B/Fluids 8 (1989) 229-268
    • (1989) Europ. J. Mech. B/Fluids , vol.8 , pp. 229-268
    • Iooss, G.1    Mielke, A.2    Demay, Y.3
  • 79
  • 80
    • 0002137866 scopus 로고
    • Long wave asymptotics, integrable equations as asymptotic limits of non-linear systems
    • Kalyakin L.A. Long wave asymptotics, integrable equations as asymptotic limits of non-linear systems. Russian Math. Surveys 44 (1989) 3-42
    • (1989) Russian Math. Surveys , vol.44 , pp. 3-42
    • Kalyakin, L.A.1
  • 81
    • 84990652766 scopus 로고
    • On the nonlinear stability of plane waves for the Ginzburg-Landau equation
    • Kapitula T. On the nonlinear stability of plane waves for the Ginzburg-Landau equation. Comm. Pure Appl. Math. 47 (1994) 831-841
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 831-841
    • Kapitula, T.1
  • 82
    • 0001969945 scopus 로고    scopus 로고
    • Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation
    • Kapitula T. Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation. Nonlinearity 9 (1996) 669-685
    • (1996) Nonlinearity , vol.9 , pp. 669-685
    • Kapitula, T.1
  • 83
    • 22044432300 scopus 로고    scopus 로고
    • Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation
    • Kapitula T. Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation. Proc. Roy. Soc. Edinburgh Ser. A 128 (1998) 585-629
    • (1998) Proc. Roy. Soc. Edinburgh Ser. A , vol.128 , pp. 585-629
    • Kapitula, T.1
  • 84
    • 0000127722 scopus 로고    scopus 로고
    • Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation
    • Kapitula T., and Maier-Paape S. Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation. Zeits. Angew. Math. Physik (ZAMP) 47 (1996) 265-305
    • (1996) Zeits. Angew. Math. Physik (ZAMP) , vol.47 , pp. 265-305
    • Kapitula, T.1    Maier-Paape, S.2
  • 85
    • 0002348145 scopus 로고    scopus 로고
    • Stability of bright and dark solitary-wave solutions to perturbed nonlinear Schrödinger equations
    • Kapitula T., and Sandstede B. Stability of bright and dark 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
  • 86
    • 85058498284 scopus 로고
    • Berechnung der Verzweigungslösungen eines hydrodynamischen Randwertproblems
    • Kirchgässner K. Berechnung der Verzweigungslösungen eines hydrodynamischen Randwertproblems. Zeits. Angew. Math. Mech. (ZAMM) 43 (1966) T61-T63
    • (1966) Zeits. Angew. Math. Mech. (ZAMM) , vol.43
    • Kirchgässner, K.1
  • 87
    • 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
  • 88
    • 4244094556 scopus 로고
    • Waves in weakly-coupled parabolic systems
    • Nonlinear Analysis and Optimization. Vinti C. (Ed), Springer, Berlin
    • Kirchgässner K. Waves in weakly-coupled parabolic systems. In: Vinti C. (Ed). Nonlinear Analysis and Optimization. Lecture Notes in Math. Vol. 1107 (1984), Springer, Berlin 154-180
    • (1984) Lecture Notes in Math. , vol.1107 , pp. 154-180
    • Kirchgässner, K.1
  • 89
    • 4243424932 scopus 로고
    • Stability analysis of branching solutions of the Navier-Stokes equations
    • Hétenyi M., and Vincenti G. (Eds), Springer, Berlin
    • Kirchgässner K., and Sorger P. Stability analysis of branching solutions of the Navier-Stokes equations. In: Hétenyi M., and Vincenti G. (Eds). Proceedings of the 12th Congress of Appl. Mechanics (Stanford 1968) (1969), Springer, Berlin 257-268
    • (1969) Proceedings of the 12th Congress of Appl. Mechanics (Stanford 1968) , pp. 257-268
    • Kirchgässner, K.1    Sorger, P.2
  • 90
    • 84971162773 scopus 로고
    • The validity of modulation equations for extended systems with cubic nonlinearities
    • Kirrmann P., Schneider G., and Mielke A. The validity of modulation equations for extended systems with cubic nonlinearities. Proc. Roy. Soc. Edinburgh Ser. A 122 (1992) 85-91
    • (1992) Proc. Roy. Soc. Edinburgh Ser. A , vol.122 , pp. 85-91
    • Kirrmann, P.1    Schneider, G.2    Mielke, A.3
  • 91
    • 0000781993 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation as a model problem
    • Dynam-ical Systems and Probabilistic Methods in Partial Differential Equations. Deift P., Levermore C.D., and Wayne C.E. (Eds), Amer. Math. Soc., Providence, RI
    • Levermore C.D., and Oliver M. The complex Ginzburg-Landau equation as a model problem. In: Deift P., Levermore C.D., and Wayne C.E. (Eds). Dynam-ical Systems and Probabilistic Methods in Partial Differential Equations. Lect. Appl. Math. Vol. 31 (1996), Amer. Math. Soc., Providence, RI 141-190
    • (1996) Lect. Appl. Math. , vol.31 , pp. 141-190
    • Levermore, C.D.1    Oliver, M.2
  • 92
    • 0000873295 scopus 로고    scopus 로고
    • Distribution-valued initial data for the complex Ginzburg-Landau equa-tion
    • Levermore C.D., and Oliver M. Distribution-valued initial data for the complex Ginzburg-Landau equa-tion. Comm. Partial Differential Equations 22 (1997) 39-48
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 39-48
    • Levermore, C.D.1    Oliver, M.2
  • 93
    • 0033248349 scopus 로고    scopus 로고
    • On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation
    • Lin F.-H., and Xin J.X. On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation. Comm. Math. Phys. 200 (1999) 249-274
    • (1999) Comm. Math. Phys. , vol.200 , pp. 249-274
    • Lin, F.-H.1    Xin, J.X.2
  • 94
    • 0005320429 scopus 로고
    • Scaling of turbulent spike amplitudes in the complex Ginzburg-Landau equa-tion
    • Luce B.P., and Doering C.R. Scaling of turbulent spike amplitudes in the complex Ginzburg-Landau equa-tion. Phys. Lett. A 178 (1993) 92-98
    • (1993) Phys. Lett. A , vol.178 , pp. 92-98
    • Luce, B.P.1    Doering, C.R.2
  • 96
    • 0002256483 scopus 로고
    • Coupled nonlocal complex Ginzburg-Landau equations in gasless com-bustion
    • Matkovsky B.J., and Volpert V. Coupled nonlocal complex Ginzburg-Landau equations in gasless com-bustion. Phys. D 54 (1992) 203-219
    • (1992) Phys. D , vol.54 , pp. 203-219
    • Matkovsky, B.J.1    Volpert, V.2
  • 97
    • 0009940282 scopus 로고    scopus 로고
    • Derivation of the time-dependent Ginzburg-Landau equation on the line
    • Melbourne I. Derivation of the time-dependent Ginzburg-Landau equation on the line. J. Nonlinear Sci. 8 (1998) 1-15
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 1-15
    • Melbourne, I.1
  • 98
    • 0002801503 scopus 로고
    • Reduction of quasilinear elliptic equations in cylindrical domains with applications
    • Mielke A. Reduction of quasilinear elliptic equations in cylindrical domains with applications. Math. Meth. Appl. Sci. 10 (1988) 51-66
    • (1988) Math. Meth. Appl. Sci. , vol.10 , pp. 51-66
    • Mielke, A.1
  • 99
    • 0039677855 scopus 로고
    • Reduction of PDEs on domains with several unbounded directions: a first step towards modu-lation equations
    • Mielke A. Reduction of PDEs on domains with several unbounded directions: a first step towards modu-lation equations. Zeits. Angew. Math. Phys. (ZAMP) 43 (1992) 449-470
    • (1992) Zeits. Angew. Math. Phys. (ZAMP) , vol.43 , pp. 449-470
    • Mielke, A.1
  • 100
    • 0009451387 scopus 로고
    • A new approach to sideband-instabilities using the principle of reduced instability
    • Nonlinear Dynamics and Pattern Formation in Natural Environment. Doelman A., and Harten A.v. (Eds), Longman, Harlow
    • Mielke A. A new approach to sideband-instabilities using the principle of reduced instability. In: Doelman A., and Harten A.v. (Eds). Nonlinear Dynamics and Pattern Formation in Natural Environment. Pitman Res. Notes Vol. 335 (1995), Longman, Harlow 206-222
    • (1995) Pitman Res. Notes , vol.335 , pp. 206-222
    • Mielke, A.1
  • 101
    • 0000857725 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation on large and unbounded domains: sharper bounds and attractors
    • Mielke A. The complex Ginzburg-Landau equation on large and unbounded domains: sharper bounds and attractors. Nonlinearity 10 (1997) 199-222
    • (1997) Nonlinearity , vol.10 , pp. 199-222
    • Mielke, A.1
  • 102
    • 0009450599 scopus 로고    scopus 로고
    • Mathematical analysis of sideband instabilities with application to Rayleigh-Bénard convec-tion
    • Mielke A. Mathematical analysis of sideband instabilities with application to Rayleigh-Bénard convec-tion. J. Nonlinear Sci. 7 (1997) 57-99
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 57-99
    • Mielke, A.1
  • 103
    • 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
  • 104
    • 0000491623 scopus 로고    scopus 로고
    • Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters
    • Mielke A. Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters. Phys. D 117 (1998) 106-116
    • (1998) Phys. D , vol.117 , pp. 106-116
    • Mielke, A.1
  • 105
    • 67649328063 scopus 로고    scopus 로고
    • Exponentially weighted L∞ -estimates and attractors for parabolic systems on unbounded do-mains
    • Berlin. August 1999. Fiedler B., Gröger K., and Sprekels J. (Eds), World Scientific, Singapore
    • Berlin. Mielke A. Exponentially weighted L∞ -estimates and attractors for parabolic systems on unbounded do-mains. August 1999. In: Fiedler B., Gröger K., and Sprekels J. (Eds). Proceedings of the EQUADIFF 1999 (2000), World Scientific, Singapore 641-646
    • (2000) Proceedings of the EQUADIFF 1999 , pp. 641-646
    • Mielke, A.1
  • 106
    • 0346367597 scopus 로고    scopus 로고
    • Global existence for an optical fiber laser model
    • Mielke A., Holmes P., and Kutz J.N. Global existence for an optical fiber laser model. Nonlinearity 11 (1998) 1489-1504
    • (1998) Nonlinearity , vol.11 , pp. 1489-1504
    • Mielke, A.1    Holmes, P.2    Kutz, J.N.3
  • 107
    • 67649309341 scopus 로고
    • Mielke A., and Kirchgässner K. (Eds), World Scientific, Singapore
    • In: Mielke A., and Kirchgässner K. (Eds). Structure and Dynamics of Nonlinear Waves in Fluids (1995), World Scientific, Singapore
    • (1995) Structure and Dynamics of Nonlinear Waves in Fluids
  • 108
    • 0000454926 scopus 로고
    • Attractors for modulation equations on unbounded domains-existence and comparison
    • Mielke A., and Schneider G. Attractors for modulation equations on unbounded domains-existence and comparison. Nonlinearity 8 (1995) 743-768
    • (1995) Nonlinearity , vol.8 , pp. 743-768
    • Mielke, A.1    Schneider, G.2
  • 109
    • 0001099741 scopus 로고    scopus 로고
    • Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation
    • Dynamical Systems and Probabilistic Methods in Partial Differential Equations. Deift P., Levermore C.D., and Wayne C.E. (Eds), Amer. Math. Soc., Providence, RI
    • Mielke A., and Schneider G. Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation. In: Deift P., Levermore C.D., and Wayne C.E. (Eds). Dynamical Systems and Probabilistic Methods in Partial Differential Equations. Lect. Appl. Math. Vol. 31 (1996), Amer. Math. Soc., Providence, RI 191-216
    • (1996) Lect. Appl. Math. , vol.31 , pp. 191-216
    • Mielke, A.1    Schneider, G.2
  • 111
    • 0040198048 scopus 로고    scopus 로고
    • Comparison of inertial manifolds and application to modulated systems
    • Mielke A., Schneider G., and Ziegra A. Comparison of inertial manifolds and application to modulated systems. Math. Nachrichten 214 (2000) 53-69
    • (2000) Math. Nachrichten , vol.214 , pp. 53-69
    • Mielke, A.1    Schneider, G.2    Ziegra, A.3
  • 112
    • 0000873856 scopus 로고
    • Envelope equations
    • Nonlinear Wave Motion, Amer. Math. Soc., Providence, RI
    • Newell A.C. Envelope equations. Nonlinear Wave Motion. Lectures in Appl. Math. Vol. 15 (1974), Amer. Math. Soc., Providence, RI 157-163
    • (1974) Lectures in Appl. Math. , vol.15 , pp. 157-163
    • Newell, A.C.1
  • 114
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • Newell A., and Whitehead J. Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38 (1969) 279-303
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newell, A.1    Whitehead, J.2
  • 116
    • 0043043828 scopus 로고    scopus 로고
    • The Ginzburg-Landau equation III. Vortex dynamics
    • Ovchinnikov Y.N., and Sigal I.M. The Ginzburg-Landau equation III. Vortex dynamics. Nonlinearity 11 (1998) 1277-1294
    • (1998) Nonlinearity , vol.11 , pp. 1277-1294
    • Ovchinnikov, Y.N.1    Sigal, I.M.2
  • 117
    • 0037702438 scopus 로고    scopus 로고
    • A global existence result for a spatially extended 3D Navier-Stokes problem with non-small initial data
    • Peterhof D., and Schneider G. A global existence result for a spatially extended 3D Navier-Stokes problem with non-small initial data. Nonlinear Differential Equations Appl. (NoDEA) 7 (2000) 415-434
    • (2000) Nonlinear Differential Equations Appl. (NoDEA) , vol.7 , pp. 415-434
    • Peterhof, D.1    Schneider, G.2
  • 118
    • 0038815248 scopus 로고    scopus 로고
    • Global attractors in partial differential equations
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Raugel G. Global attractors in partial differential equations. In: Fiedler B. (Ed). Handbook in Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 885-982
    • (2002) Handbook in Dynamical Systems , vol.2 , pp. 885-982
    • Raugel, G.1
  • 120
    • 0003740409 scopus 로고    scopus 로고
    • Stability, Instability, and Direct Integrals
    • Chapman and Hall/CRC
    • Scarpellini B. Stability, Instability, and Direct Integrals. Pitman Res. Notes in Math. Vol. 402 (1999), Chapman and Hall/CRC
    • (1999) Pitman Res. Notes in Math. , vol.402
    • Scarpellini, B.1
  • 121
    • 0031238210 scopus 로고    scopus 로고
    • On the validity of the degenerate Ginzburg-Landau equation
    • Shepeleva A. On the validity of the degenerate Ginzburg-Landau equation. Math. Meth. Appl. Sci. 20 (1997) 1239-1256
    • (1997) Math. Meth. Appl. Sci. , vol.20 , pp. 1239-1256
    • Shepeleva, A.1
  • 122
    • 3342970503 scopus 로고    scopus 로고
    • Modulated modulation approach to the loss of stability of periodic solutions for the degen-erate Ginzburg-Landau equation
    • Shepeleva A. Modulated modulation approach to the loss of stability of periodic solutions for the degen-erate Ginzburg-Landau equation. Nonlinearity 11 (1998) 409-429
    • (1998) Nonlinearity , vol.11 , pp. 409-429
    • Shepeleva, A.1
  • 123
    • 67649350539 scopus 로고    scopus 로고
    • Subcritical bifurcation to infinitely many rotating waves
    • (to ap-pear)
    • (to ap-pear). Scheel A. Subcritical bifurcation to infinitely many rotating waves. J. Math. Anal. Appl. (1998)
    • (1998) J. Math. Anal. Appl.
    • Scheel, A.1
  • 124
    • 0032361995 scopus 로고    scopus 로고
    • Bifurcation to spiral waves in reaction-diffusion systems
    • (to appear)
    • (to appear). Scheel A. Bifurcation to spiral waves in reaction-diffusion systems. SIAM J. Math. Anal. (1999)
    • (1999) SIAM J. Math. Anal.
    • Scheel, A.1
  • 125
    • 0027929634 scopus 로고
    • A new estimate for the Ginzburg-Landau approximation on the real axis
    • Schneider G. A new estimate for the Ginzburg-Landau approximation on the real axis. J. Nonlinear Sci. 4 (1994) 23-34
    • (1994) J. Nonlinear Sci. , vol.4 , pp. 23-34
    • Schneider, G.1
  • 126
    • 0001656215 scopus 로고
    • Error estimates for the Ginzburg-Landau approximation
    • Schneider G. Error estimates for the Ginzburg-Landau approximation. Zeits. Angew. Math. Phys. (ZAMP) 45 (1994) 433-457
    • (1994) Zeits. Angew. Math. Phys. (ZAMP) , vol.45 , pp. 433-457
    • Schneider, G.1
  • 127
    • 21344476138 scopus 로고
    • Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations
    • Schneider G. Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Comm. Math. Phys. 164 (1994) 157-179
    • (1994) Comm. Math. Phys. , vol.164 , pp. 157-179
    • Schneider, G.1
  • 128
    • 0001492119 scopus 로고
    • Analyticity of Ginzburg-Landau modes
    • Schneider G. Analyticity of Ginzburg-Landau modes. J. Differential Equations 121 (1995) 233-257
    • (1995) J. Differential Equations , vol.121 , pp. 233-257
    • Schneider, G.1
  • 129
    • 84985386714 scopus 로고
    • Validity and limitation of the Newell-Whitehead equation
    • Schneider G. Validity and limitation of the Newell-Whitehead equation. Math. Nachrichten 176 (1995) 249-263
    • (1995) Math. Nachrichten , vol.176 , pp. 249-263
    • Schneider, G.1
  • 130
    • 0345099992 scopus 로고
    • Justification of modulation equations in domains with n≥2 unbounded space directions
    • Mielke A., and Kirchgässner K. (Eds), World Scien-tific, Singapore
    • Schneider G. Justification of modulation equations in domains with n≥2 unbounded space directions. In: Mielke A., and Kirchgässner K. (Eds). Structure and Dynamics of Nonlinear Waves in Fluids (1995), World Scien-tific, Singapore 383-391
    • (1995) Structure and Dynamics of Nonlinear Waves in Fluids , pp. 383-391
    • Schneider, G.1
  • 131
    • 0030170151 scopus 로고    scopus 로고
    • The validity of generalized Ginzburg-Landau equations
    • Schneider G. The validity of generalized Ginzburg-Landau equations. Math. Methods Appl. Sci. 19 (1996) 717-736
    • (1996) Math. Methods Appl. Sci. , vol.19 , pp. 717-736
    • Schneider, G.1
  • 132
    • 33747017391 scopus 로고    scopus 로고
    • Justification of mean-field coupled modulation equations
    • Schneider G. Justification of mean-field coupled modulation equations. Proc. Roy. Soc. Edinburgh Ser. A 127 (1997) 639-650
    • (1997) Proc. Roy. Soc. Edinburgh Ser. A , vol.127 , pp. 639-650
    • Schneider, G.1
  • 133
    • 0039500618 scopus 로고    scopus 로고
    • Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation
    • Schneider G. Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. J. Differential Equations 147 (1998) 333-354
    • (1998) J. Differential Equations , vol.147 , pp. 333-354
    • Schneider, G.1
  • 134
    • 0009072272 scopus 로고    scopus 로고
    • Hopf-bifurcation in spatially extended reaction-diffusion systems
    • Schneider G. Hopf-bifurcation in spatially extended reaction-diffusion systems. J. Nonlinear Sci. 8 (1998) 17-41
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 17-41
    • Schneider, G.1
  • 135
    • 0007015954 scopus 로고    scopus 로고
    • Justification of modulation equations for hyperbolic systems via normal forms
    • Schneider G. Justification of modulation equations for hyperbolic systems via normal forms. Nonlinear Differential Equations Appl. (NoDEA) 5 (1998) 69-82
    • (1998) Nonlinear Differential Equations Appl. (NoDEA) , vol.5 , pp. 69-82
    • Schneider, G.1
  • 136
    • 0032344332 scopus 로고    scopus 로고
    • Nonlinear stability of Taylor vortices in infinite cylinders
    • Schneider G. Nonlinear stability of Taylor vortices in infinite cylinders. Arch. Rational Mech. Anal. 144 (1998) 121-200
    • (1998) Arch. Rational Mech. Anal. , vol.144 , pp. 121-200
    • Schneider, G.1
  • 137
    • 22844454067 scopus 로고    scopus 로고
    • Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an un-bounded domain
    • Schneider G. Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an un-bounded domain. Zeits. Angew. Math. Mech. (ZAMM) 79 (1999) 615-626
    • (1999) Zeits. Angew. Math. Mech. (ZAMM) , vol.79 , pp. 615-626
    • Schneider, G.1
  • 138
    • 0033548773 scopus 로고    scopus 로고
    • Global existence results for pattern forming processes in infinite cylindrical domains-Applications to 3D Navier-Stokes problems
    • Schneider G. Global existence results for pattern forming processes in infinite cylindrical domains-Applications to 3D Navier-Stokes problems. J. Math. Pures Appl. 78 (1999) 265-312
    • (1999) J. Math. Pures Appl. , vol.78 , pp. 265-312
    • Schneider, G.1
  • 139
    • 33947265459 scopus 로고    scopus 로고
    • Some characterizations of the Taylor-Couette attractor
    • Schneider G. Some characterizations of the Taylor-Couette attractor. Integral Differential Equations 12 (1999) 913-926
    • (1999) Integral Differential Equations , vol.12 , pp. 913-926
    • Schneider, G.1
  • 140
    • 0014560133 scopus 로고
    • Distant sidewalls cause slow amplitude modulation of cellular convection
    • Segel L.A. Distant sidewalls cause slow amplitude modulation of cellular convection. J. Fluid Mech. 38 (1969) 203-224
    • (1969) J. Fluid Mech. , vol.38 , pp. 203-224
    • Segel, L.A.1
  • 142
    • 84959644006 scopus 로고
    • A nonlinear instability theory for a wave system in a plane Poiseuille flow
    • Stewartson K., and Stuart J.T. A nonlinear instability theory for a wave system in a plane Poiseuille flow. J. Fluid Mech. 48 (1971) 529-545
    • (1971) J. Fluid Mech. , vol.48 , pp. 529-545
    • Stewartson, K.1    Stuart, J.T.2
  • 143
    • 0017983543 scopus 로고
    • The Eckhaus and the Benjamin-Feir resonance mechanisms
    • Stuart J.T., and DiPrima R.C. The Eckhaus and the Benjamin-Feir resonance mechanisms. Proc. Roy. Soc. London Ser. A 363 (1978) 27-41
    • (1978) Proc. Roy. Soc. London Ser. A , vol.363 , pp. 27-41
    • Stuart, J.T.1    DiPrima, R.C.2
  • 145
    • 0001545279 scopus 로고
    • On the validity of Ginzburg-Landau's equation
    • Harten A.v. On the validity of Ginzburg-Landau's equation. J. Nonlinear Sci. 1 (1991) 397-422
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 397-422
    • Harten, A.v.1
  • 146
    • 3342956197 scopus 로고
    • Modulated modulation equations
    • Mielke A., and Kirchgässner K. (Eds), World Scientific, Singapore
    • Harten A.v. Modulated modulation equations. In: Mielke A., and Kirchgässner K. (Eds). Structure and Dynamics of Nonlinear Waves in Fluids (1995), World Scientific, Singapore 117-130
    • (1995) Structure and Dynamics of Nonlinear Waves in Fluids , pp. 117-130
    • Harten, A.v.1
  • 147
    • 44049115047 scopus 로고
    • Fronts, pulses, sources and sinks in generalised complex Ginzburg-Landau equations
    • Saarloos W.v., and Hohenberg P.C. Fronts, pulses, sources and sinks in generalised complex Ginzburg-Landau equations. Phys. D 56 (1992) 303-367
    • (1992) Phys. D , vol.56 , pp. 303-367
    • Saarloos, W.v.1    Hohenberg, P.C.2
  • 148
    • 0030500197 scopus 로고    scopus 로고
    • Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations
    • Weinstein M.I., and Xin J. Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations. Comm. Math. Phys. 180 (1996) 389-428
    • (1996) Comm. Math. Phys. , vol.180 , pp. 389-428
    • Weinstein, M.I.1    Xin, J.2
  • 149
    • 22244432207 scopus 로고    scopus 로고
    • Numerically derived scalings for the complex Ginzburg-Landau equation
    • Wilson R.E. Numerically derived scalings for the complex Ginzburg-Landau equation. Phys. D 112 (1998) 329-343
    • (1998) Phys. D , vol.112 , pp. 329-343
    • Wilson, R.E.1
  • 150
    • 67649325548 scopus 로고    scopus 로고
    • Personal communication, Bath April
    • R.E. Wilson, Personal communication, Bath (April 1999).
    • (1999)
    • Wilson, R.E.1
  • 151
    • 0003005007 scopus 로고
    • Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
    • Zakharov V.E., and Kuznetsov E.A. Multi-scale expansions in the theory of systems integrable by the inverse scattering transform. Phys. D 18 (1986) 455-463
    • (1986) Phys. D , vol.18 , pp. 455-463
    • Zakharov, V.E.1    Kuznetsov, E.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.