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Volumn 8, Issue 1, 1998, Pages 1-15

Derivation of the Time-Dependent Ginzburg-Landau Equation on the Line

Author keywords

Bifurcation theory; Euclidean symmetry; Ginzburg Landau equation; Normal form symmetry

Indexed keywords


EID: 0009940282     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329900041     Document Type: Article
Times cited : (38)

References (26)
  • 1
    • 0027009632 scopus 로고
    • Uniformly traveling water from a dynamical systems viewpoint: Some insight into bifurcations from the Stokes family
    • C. Baesens and R. S. Mackay. Uniformly traveling water from a dynamical systems viewpoint: Some insight into bifurcations from the Stokes family. J. Fluid Mech. 241 (1992), 333-347.
    • (1992) J. Fluid Mech. , vol.241 , pp. 333-347
    • Baesens, C.1    Mackay, R.S.2
  • 2
    • 0000484304 scopus 로고
    • The time dependent amplitude equation for the Swift-Hohenberg problem
    • P. Collet and J.P. Eckmann. The time dependent amplitude equation for the Swift-Hohenberg problem. Commun. Math. Phys. 132 (1990), 139-153.
    • (1990) Commun. Math. Phys. , vol.132 , pp. 139-153
    • Collet, P.1    Eckmann, J.P.2
  • 4
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M. C. Cross and P. C. Hohenberg. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65 (1993), 851-1112.
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 5
    • 84959666786 scopus 로고
    • Nonlinear wave-number interaction in near-critical two-dimensional flows
    • R. C. DiPrima, W. Eckhaus, and L. A. Segel. Nonlinear wave-number 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.A.3
  • 6
    • 0003263144 scopus 로고
    • Singularities and Groups in Bifurcation Theory
    • Springer, New York
    • M. Golubitsky and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory, Vol. 1. Appl. Math. Sci. 51, Springer, New York, 1984.
    • (1984) Appl. Math. Sci. , vol.1-51
    • Golubitsky, M.1    Schaeffer, D.G.2
  • 7
    • 0003285244 scopus 로고
    • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
    • Springer, New York
    • J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Appl. Math. Sci. 42, Springer, New York, 1983.
    • (1983) Appl. Math. Sci. , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 8
    • 0001545279 scopus 로고
    • On the validity of the Ginzburg-Landau equation
    • A. van Harten. On the validity of the Ginzburg-Landau equation. J. Nonlin. Sci. 1 (1991), 397-422.
    • (1991) J. Nonlin. Sci. , vol.1 , pp. 397-422
    • Van Harten, A.1
  • 10
    • 0013367883 scopus 로고
    • Bifurcation of spatially quasiperiodic solutions in hydrodynamic stability problems
    • G. Iooss and J. Los. Bifurcation of spatially quasiperiodic solutions in hydrodynamic stability problems. Nonlinearity 3 (1990), 851-871.
    • (1990) Nonlinearity , vol.3 , pp. 851-871
    • Iooss, G.1    Los, J.2
  • 11
    • 0000677116 scopus 로고
    • Theory of steady Ginzburg-Landau equation in hydrodynamic stability problems
    • G. Iooss, A. Mielke, and Y. Demay. Theory of steady Ginzburg-Landau equation in hydrodynamic stability problems. Eur. J. Mech., B/Fluids 8 (1989), 229-268.
    • (1989) Eur. J. Mech., B/Fluids , vol.8 , pp. 229-268
    • Iooss, G.1    Mielke, A.2    Demay, Y.3
  • 13
    • 49049138209 scopus 로고
    • Wave solutions of reversible systems and applications
    • K. Kirchgässner. Wave solutions of reversible systems and applications. J. Diff. Eq. 45 (1982), 113-127.
    • (1982) J. Diff. Eq. , vol.45 , pp. 113-127
    • Kirchgässner, K.1
  • 14
    • 84971162773 scopus 로고
    • The validity of modulation equations for extended systems with cubic nonlinearities
    • P. Kirrmann, G. Schneider, and A. Mielke. The validity of modulation equations for extended systems with cubic nonlinearities. Proc. Roy. Soc. Edinburgh A 122 (1992), 85-91.
    • (1992) Proc. Roy. Soc. Edinburgh A , vol.122 , pp. 85-91
    • Kirrmann, P.1    Schneider, G.2    Mielke, A.3
  • 15
    • 85033900191 scopus 로고    scopus 로고
    • Steady-state bifurcation with Euclidean symmetry
    • To appear
    • I. Melbourne. Steady-state bifurcation with Euclidean symmetry. To appear in Trans. Am. Math. Soc.
    • Trans. Am. Math. Soc.
    • Melbourne, I.1
  • 16
    • 3643098187 scopus 로고
    • A reduction principle for nonautonomous systems in infinite dimensional spaces
    • A. Mielke. A reduction principle for nonautonomous systems in infinite dimensional spaces. J. Diff. Eq. 65 (1986), 68-88.
    • (1986) J. Diff. Eq. , vol.65 , pp. 68-88
    • Mielke, A.1
  • 17
    • 38249041215 scopus 로고
    • Steady flows of inviscid fluids under localized perturbations
    • A. Mielke. Steady flows of inviscid fluids under localized perturbations. J. Diff. Eq. 65 (1986), 89-116.
    • (1986) J. Diff. Eq. , vol.65 , pp. 89-116
    • Mielke, A.1
  • 18
    • 0002801503 scopus 로고
    • Reduction of quasilinear elliptic equations in cylindrical domains with applications
    • A. Mielke. 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
  • 19
    • 0039677855 scopus 로고
    • Reduction of PDEs on domains with several unbounded directions: A first step towards modulation equations
    • A. Mielke. Reduction of PDEs on domains with several unbounded directions: A first step towards modulation equations. Z. Angew. Math. Phys. 43 (1992) 449-470.
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 449-470
    • Mielke, A.1
  • 20
    • 0038946525 scopus 로고
    • The dynamics and analysis of patterns
    • Addison-Wesley, New York
    • A. C. Newell. The dynamics and analysis of patterns. In Lectures in the Sciences of Complexity 1, Addison-Wesley, New York, 1989, 107-173.
    • (1989) Lectures in the Sciences of Complexity , vol.1 , pp. 107-173
    • Newell, A.C.1
  • 21
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • A. C. Newell and J. A. Whitehead. Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38 (1969), 279-303.
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newell, A.C.1    Whitehead, J.A.2
  • 22
    • 0009905306 scopus 로고
    • Nonadiabatic phenomena in cellular structures
    • (J. Wesfried and S. Zalesky, eds.), Springer, New York
    • Y. Pomeau. Nonadiabatic phenomena in cellular structures. In Cellular Structures in Instabilities (J. Wesfried and S. Zalesky, eds.), Springer, New York, 1984, 207-214.
    • (1984) Cellular Structures in Instabilities , pp. 207-214
    • Pomeau, Y.1
  • 23
    • 0346497244 scopus 로고
    • Stability and self-organization in open systems
    • (G. Nicolis and R. Lefever, eds.), Wiley, New York
    • I. Prigogine and R. Lefever. Stability and self-organization in open systems. In Membranes, Dissipative Structures and Evolution (G. Nicolis and R. Lefever, eds.), Wiley, New York, 1974, 215-240.
    • (1974) Membranes, Dissipative Structures and Evolution , pp. 215-240
    • Prigogine, I.1    Lefever, R.2
  • 24
    • 0027929634 scopus 로고
    • A new estimate for the Ginzburg-Landau approximation on the real axix
    • G. Schneider. A new estimate for the Ginzburg-Landau approximation on the real axix. J. Nonlin. Sci. 4 (1994), 23-34.
    • (1994) J. Nonlin. Sci. , vol.4 , pp. 23-34
    • Schneider, G.1
  • 25
    • 0001656215 scopus 로고
    • Error estimates for the Ginzburg-Landau approximation
    • G. Schneider. Error estimates for the Ginzburg-Landau approximation. Z. Angew. Math. Phys. 45 (1994), 433-457.
    • (1994) Z. Angew. Math. Phys. , vol.45 , pp. 433-457
    • Schneider, G.1
  • 26
    • 0014560133 scopus 로고
    • Distant side-walls cause slow amplitude modulation of cellular convection
    • L. A. Segel. Distant side-walls 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.