메뉴 건너뛰기




Volumn 118, Issue 3-4, 1998, Pages 261-292

On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation

Author keywords

Degenerations; Modulation equations; Nonlinear stability; Numerical simulations

Indexed keywords


EID: 0000311228     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00035-9     Document Type: Article
Times cited : (43)

References (35)
  • 1
    • 0028443125 scopus 로고
    • Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
    • J.G. Blom, P.A. Zegeling, Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations, ACM Trans. Math. Software 20 (1994) 194-214.
    • (1994) ACM Trans. Math. Software , vol.20 , pp. 194-214
    • Blom, J.G.1    Zegeling, P.A.2
  • 2
    • 0001726540 scopus 로고
    • On electrically driven pattern-forming instabilities in planar nematics
    • France
    • E. Bodenschatz, W. Zimmerman, L. Kramer, On electrically driven pattern-forming instabilities in planar nematics, J. Phys. (France) 49 (1988) 1875-1899.
    • (1988) J. Phys. , vol.49 , pp. 1875-1899
    • Bodenschatz, E.1    Zimmerman, W.2    Kramer, L.3
  • 4
    • 53349120754 scopus 로고    scopus 로고
    • Bifurcation and coalescence of a plethora of homoclinic orbits for a hamiltonian system
    • B. Buffoni, A.R. Champneys, J.F. Toland, Bifurcation and coalescence of a plethora of homoclinic orbits for a hamiltonian system, J. Dyn. Diff. Eq. 8 (1996) 221-279.
    • (1996) J. Dyn. Diff. Eq. , vol.8 , pp. 221-279
    • Buffoni, B.1    Champneys, A.R.2    Toland, J.F.3
  • 5
    • 0000484304 scopus 로고
    • The time-dependent amplitude equation for the Swift-Hohenberg problem
    • P. Collet, J.P. Eckman, 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    Eckman, J.P.2
  • 8
    • 0000689240 scopus 로고
    • Bistable systems with propagating fronts leading to pattern formation
    • G.T. Dee, W. van Saarloos, Bistable systems with propagating fronts leading to pattern formation, Phys. Rev. Lett. 60 (1988) 2641-2644.
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 2641-2644
    • Dee, G.T.1    Van Saarloos, W.2
  • 9
    • 0000238802 scopus 로고
    • Periodic and quasi-periodic solutions of degenerate modulation equations
    • A. Doelman, W. Eckhaus, Periodic and quasi-periodic solutions of degenerate modulation equations, Physica D 53 (1991) 249-266.
    • (1991) Physica D , vol.53 , pp. 249-266
    • Doelman, A.1    Eckhaus, W.2
  • 10
    • 0000706319 scopus 로고    scopus 로고
    • Pattern formation in the one-dimensional Gray-Scott model
    • A. Doelman, T.J. Kaper, P.A. Zegeling, Pattern formation in the one-dimensional Gray-Scott model, Nonlinearity 10 (1997) 523-563.
    • (1997) Nonlinearity , vol.10 , pp. 523-563
    • Doelman, A.1    Kaper, T.J.2    Zegeling, P.A.3
  • 11
    • 0009268172 scopus 로고    scopus 로고
    • Singularly perturbed and non-local modulation equations for system with interacting instability mechanisms
    • A. Doelman, V. Rottschäfer, Singularly perturbed and non-local modulation equations for system 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
  • 16
    • 0001722258 scopus 로고
    • On modulation equations of the Ginzburg-Landau type
    • R.E. O'Malley (Ed.)
    • W. Eckhaus, On modulation equations of the Ginzburg-Landau type, in: R.E. O'Malley (Ed.), ICIAM 91: Proc. 2nd Int. Conf. Ind. Appl. Math., 1992, pp. 83-98.
    • (1992) ICIAM 91: Proc. 2nd Int. Conf. Ind. Appl. Math. , pp. 83-98
    • Eckhaus, W.1
  • 17
    • 51249162531 scopus 로고
    • The Ginzburg-Landau manifold is an attractor
    • W. Eckhaus, The Ginzburg-Landau manifold is an attractor, J. Nonlinear Sci. 3 (1992) 329-348.
    • (1992) J. Nonlinear Sci. , vol.3 , pp. 329-348
    • Eckhaus, W.1
  • 18
    • 0000810343 scopus 로고
    • Strong selection or rejection of spatially periodic patterns in degenerate bifurcations
    • W. Eckhaus, G. Iooss, Strong selection or rejection of spatially periodic patterns in degenerate bifurcations, Physica D 39 (1989) 124-146.
    • (1989) Physica D , vol.39 , pp. 124-146
    • Eckhaus, W.1    Iooss, G.2
  • 19
    • 0001545279 scopus 로고
    • On the validity of the Ginzburg-Landau's equation
    • A. van Harten, On the validity of the Ginzburg-Landau's equation J. Nonlinear Sci. 1 (1991) 397-422.
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 397-422
    • Van Harten, A.1
  • 20
    • 85044493148 scopus 로고    scopus 로고
    • Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
    • to appear
    • W.D. Kalies, J. Kwapisz, R.C.A.M. VanderVorst, Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria, Comm. Math. Phys., to appear.
    • Comm. Math. Phys.
    • Kalies, W.D.1    Kwapisz, J.2    VanderVorst, R.C.A.M.3
  • 21
    • 0030295224 scopus 로고    scopus 로고
    • Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation
    • W.D. Kalies, R.C.A.M. VanderVorst, Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation, J. Diff. Eq. 131 (1996) 209-228.
    • (1996) J. Diff. Eq. , vol.131 , pp. 209-228
    • Kalies, W.D.1    VanderVorst, R.C.A.M.2
  • 22
    • 46549092908 scopus 로고
    • On the Eckhaus instability for spatial periodic patterns
    • L. Kramer, W. Zimmerman, On the Eckhaus instability for spatial periodic patterns, Physica D 16 (1985) 221-232.
    • (1985) Physica D , vol.16 , pp. 221-232
    • Kramer, L.1    Zimmerman, W.2
  • 25
    • 0001258631 scopus 로고
    • Universal description of laser dynamics near threshold
    • J. Lega, J.V. Moloney, A.C. Newell, Universal description of laser dynamics near threshold, Physica D 83 (1995) 478-498.
    • (1995) Physica D , vol.83 , pp. 478-498
    • Lega, J.1    Moloney, J.V.2    Newell, A.C.3
  • 26
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • A.C. Newell, J.A. Whitehead, Finite bandwidth, finite amplitude convection, J. Fluid Mech. 28 (1969) 279-303.
    • (1969) J. Fluid Mech. , vol.28 , pp. 279-303
    • Newell, A.C.1    Whitehead, J.A.2
  • 27
    • 0001173202 scopus 로고    scopus 로고
    • Spatial patterns described by the extended Fisher-Kolmogorov equation: Periodic solutions
    • L.A. Peletier, W.C. Troy, Spatial patterns described by the extended Fisher-Kolmogorov equation: Periodic solutions, SIAM J. Math. Anal. 28 (1997) 1318-1353.
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 1318-1353
    • Peletier, L.A.1    Troy, W.C.2
  • 28
    • 44049115047 scopus 로고
    • Fronts, pulses, sources and sinks in generalised complex Ginzburg-Landau equations
    • W. van Saarloos, P.C. Hohenberg, Fronts, pulses, sources and sinks in generalised complex Ginzburg-Landau equations, Physica D 56 (1992) 303-367.
    • (1992) Physica D , vol.56 , pp. 303-367
    • Van Saarloos, W.1    Hohenberg, P.C.2
  • 29
    • 0009072272 scopus 로고    scopus 로고
    • Hopf-bifurcation in spatially extended reaction-diffusion systems
    • to appear
    • G. Schneider, Hopf-bifurcation in spatially extended reaction-diffusion systems, J. Nonlinear Sci., to appear.
    • J. Nonlinear Sci.
    • Schneider, G.1
  • 30
    • 84956080427 scopus 로고
    • Multicritical behaviour in binary fluid convection
    • W. Schöpf, W. Zimmerman, Multicritical behaviour in binary fluid convection, Europhys. Lett. 8 (1) (1989) 41-46.
    • (1989) Europhys. Lett. , vol.8 , Issue.1 , pp. 41-46
    • Schöpf, W.1    Zimmerman, W.2
  • 31
    • 22244453707 scopus 로고    scopus 로고
    • On the validity of the degenerate Ginzburg-Landau equation
    • to appear
    • A. Shepeleva, On the validity of the degenerate Ginzburg-Landau equation, Math. Methods Appl. Sci. (1996), to appear.
    • (1996) Math. Methods Appl. Sci.
    • Shepeleva, A.1
  • 32
    • 0000049185 scopus 로고
    • Hydrodynamic fluctuations at the convective instability
    • J. Swift, P.C. Hohenberg, Hydrodynamic fluctuations at the convective instability, Phys. Rev. A 15 (1977) 319-328.
    • (1977) Phys. Rev. A , vol.15 , pp. 319-328
    • Swift, J.1    Hohenberg, P.C.2
  • 34
    • 0000129317 scopus 로고
    • Propagating fronts near a Lifshitz point
    • W. Zimmerman, Propagating fronts near a Lifshitz point, Phys. Rev. Lett. 66 (1991) 1546.
    • (1991) Phys. Rev. Lett. , vol.66 , pp. 1546
    • Zimmerman, W.1
  • 35
    • 84956093100 scopus 로고
    • The effect of spatial modulations on codimension-2 bifurcations
    • W. Zimmerman, D. Armbruster, L. Kramer, W. Kuang, The effect of spatial modulations on codimension-2 bifurcations, Europhys. Lett. 6 (1988) 505-510.
    • (1988) Europhys. Lett. , vol.6 , pp. 505-510
    • Zimmerman, W.1    Armbruster, D.2    Kramer, L.3    Kuang, W.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.