Traveling waves in the complex Ginzburg-Landau equation
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Publication:1322784
DOI10.1007/BF02429865zbMath0805.35050MaRDI QIDQ1322784
Publication date: 30 May 1994
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
travelling wavespattern formationmodular equationsone- dimensional Ginzburg-Landau equationperturbed integrable systemstwo-parameter families of spatially quasiperiodic solutions
Nonlinear parabolic equations (35K55) Continuation and prolongation of solutions to PDEs (35B60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
Related Items (22)
Invariant Painlevé analysis and coherent structures of two families of reaction-diffusion equations ⋮ Singular heteroclinic orbits for degenerate modulation equations ⋮ Traveling fronts of a real supercritical Ginzburg-Landau equation coupled by a slow diffusion ⋮ Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms ⋮ Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation ⋮ Bifurcations of plane wave (CW) solutions in the complex cubic--quintic Ginzburg--Landau equation ⋮ The complex cubic--quintic Ginzburg--Landau equation: Hopf bifurcations yielding traveling waves ⋮ Spatiotemporal structure of pulsating solitons in the cubic-quintic Ginzburg-Landau equation: A novel variational formulation ⋮ Instability of quasiperiodic solutions of the Ginzburg–Landau equation ⋮ Application of bifurcation method and rational sine-Gordon expansion method for solving 2D complex Ginzburg–Landau equation ⋮ Standing waves of the complex Ginzburg-Landau equation ⋮ Bifurcation of homoclinic orbits to a saddle-focus in reversible systems with SO(2)-symmetry ⋮ A novel variational approach to pulsating solitons in the cubic-quintic Ginzburg-Landau equation ⋮ A novel analytic technique for the disintegration of coherent structure solutions of non-integrable and integrable nonlinear PDEs under forcing ⋮ Homoclinic and Heteroclinic Bifurcations Close to a Twisted Heteroclinic Cycle ⋮ Traveling wavetrains in the complex cubic-quintic Ginzburg-Landau equation ⋮ Breaking the hidden symmetry in the Ginzburg-Landau equation ⋮ Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation ⋮ Snake solitons in the cubic-quintic Ginzburg-Landau equation ⋮ Bifurcation to traveling waves in the cubic–quintic complex Ginzburg–Landau equation ⋮ Multipulse-like orbits for a singularly perturbed nearly integrable system. ⋮ Bifurcations and competing coherent structures in the cubic-quintic Ginzburg--Landau equation. I: Plane wave (CW) solutions
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