Breaking the hidden symmetry in the Ginzburg-Landau equation

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  W. Eckhaus.  Studies in Non-Linear Stability Theory , 1965 .

[3]  L. M. Hocking,et al.  On the Nonlinear Response of a Marginally Unstable Plane Parallel Flow to a Two-Dimensional Disturbance , 1972 .

[4]  R. C. DiPrima,et al.  The Eckhaus and Benjamin-Feir resonance mechanisms , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Neil Fenichel.  Geometric singular perturbation theory for ordinary differential equations , 1979 .

[6]  Nancy Kopell,et al.  Target Patterns and Horseshoes from a Perturbed Central-Force Problem: Some Temporally Periodic Solutions to Reaction-Diffusion Equations , 1981 .

[7]  Clark Robinson,et al.  Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients , 1983 .

[8]  W. Kath.  Slowly Varying Phase Planes and Boundary-Layer Theory , 1985 .

[9]  K. Nozaki,et al.  Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation , 1985 .

[10]  Philip Holmes.  Spatial structure of time-periodic solutions of the Ginzburg-Landau equation☆ , 1986 .

[11]  Stephen Wiggins,et al.  Global Bifurcations and Chaos , 1988 .

[12]  Wiktor Eckhaus,et al.  Strong selection or rejection of spatially periodic patterns in degenerate bifurcations , 1989 .

[13]  Arjen Doelman,et al.  Slow time-periodic solutions of the Ginzburg-Landau equation , 1989 .

[14]  A. V. Harten,et al.  On the validity of Ginzberg-Landau's equation , 1990 .

[15]  T. Kapitula,et al.  Nearly real fronts in a Ginzburg–Landau equation , 1990, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[16]  Pierre Collet,et al.  The time dependent amplitude equation for the Swift-Hohenberg problem , 1990 .

[17]  P. Kolodner,et al.  Competing and coexisting dynamical states of travelling-wave convection in an annulus , 1990, Journal of Fluid Mechanics.

[18]  T. Kapitula.  Stability of weak shocks in λ-ω systems , 1991 .

[19]  A. van Harten,et al.  On the validity of the Ginzburg-Landau equation , 1991 .

[20]  Arjen Doelman,et al.  Periodic and quasi-periodic solutions of degenerate modulation equations , 1991 .

[21]  W. Eckhaus.  On modulation equations of the Ginzburg-Landau type , 1992 .

[22]  P. C. Hohenberg,et al.  Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .

[23]  Arjen Doelman,et al.  Traveling waves in the complex Ginzburg-Landau equation , 1993 .

[24]  B. Matkowsky,et al.  Stability of plane wave solutions of complex Ginzburg-Landau equations , 1993 .

[25]  Weber,et al.  Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation. , 1993, Physical review letters.

[26]  Philippe Marcq,et al.  Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation , 1993, patt-sol/9310004.

[27]  S. Wiggins.  Normally Hyperbolic Invariant Manifolds in Dynamical Systems , 1994 .

[28]  L. Kramer,et al.  From dark solitons in the defocusing nonlinear Schro¨dinger to holes in the complex Ginzburg-Landau equation , 1994, patt-sol/9409003.

[29]  Olaf Stiller,et al.  Hole solutions in the 1D complex Ginzburg-Landau equation , 1995 .

[30]  T. Kapitula.  Singular heteroclinic orbits for degenerate modulation equations , 1995 .

[31]  A. Doelman,et al.  Nonlinear Dynamics and Pattern Formation in the Natural Environment , 1995 .

[32]  Philip Holmes,et al.  Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation , 1995, Proceedings of the Edinburgh Mathematical Society.

[33]  A. V. Harten,et al.  On the Justification of the Ginzburg-Landau approximation , 1995 .

[34]  P. Holmes,et al.  Homoclinic explosions and implosions , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[35]  Todd Kapitula,et al.  Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation , 1996 .