Bifurcations to invariant 2-tori for the complex Ginzburg-Landau equation

DOI10.1016/S0096-3003(97)81661-XzbMath0904.65101MaRDI QIDQ1126649

Peter Takáč

Publication date: 8 October 1998

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

bifurcationGinzburg-Landau equationlarge-time behaviournumerical simulationrotating wavebinary fluid mixtureBenjamin-Feir unstable regioninvariant 2-tori

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Bifurcations in context of PDEs (35B32)

Related Items (1)

Numerical continuation of invariant solutions of the complex Ginzburg-Landau equation

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Periodic solutions of the Ginzburg-Landau equation
• The Eckhaus instability for traveling waves
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• Instabilities of the Ginzburg-Landau equation: periodic solutions
• Instabilities of the Ginzburg-Landau equation. II. Secondary bifurcation
• Low-dimensional behaviour in the complex Ginzburg-Landau equation
• On the generation of waves by wind
• Finite-dimensional models of the Ginsburg-Landau equation
• Invariant 2-tori in the time-dependent Ginzburg-Landau equation
• Finite bandwidth, finite amplitude convection

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