Phase dynamics in the complex Ginzburg-Landau equation

DOI10.1016/j.jde.2003.11.004zbMath1059.35139OpenAlexW1970706018MaRDI QIDQ1883109

Ian Melbourne, Guido Schneider

Publication date: 1 October 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.11.004

zbMATH Keywords

pattern formationconservation lawApproximationcomplex Ginzburg-Landau equation

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Hyperbolic conservation laws (35L65) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Explicit and implicit solutions for the one-dimensional cubic and quintic complex Ginzburg-Landau equations ⋮ The Validity of Whitham's Approximation for a Klein--Gordon--Boussinesq Model ⋮ Validity of Whitham's modulation equations for dissipative systems with a conservation law: Phase dynamics in a generalized Ginzburg-Landau system ⋮ Lagrangian reduction and wave mean flow interaction ⋮ Modulation Equations Near the Eckhaus Boundary: The KdV Equation ⋮ A waiting time phenomenon for modulations of pattern in reaction-diffusion systems ⋮ Validity of the Cahn-Hilliard approximation for modulations of slightly unstable pattern in the real Ginzburg-Landau equation ⋮ Validity of Whitham's equations for the modulation of periodic traveling waves in the NLS equation ⋮ Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation

Cites Work

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• Singularities and groups in bifurcation theory. Volume II
• Global existence results for pattern forming processes in infinite cylindrical domains -- applications to 3D Navier-Stokes problems
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• Derivation of the time-dependent Ginzburg-Landau equation on the line
• The time dependent amplitude equation for the Swift-Hohenberg problem
• The dynamics of modulated wave trains
• Slowly Varying Waves and Shock Structures in Reaction-Diffusion Equations
• Steady-state bifurcation with Euclidean symmetry
• Phase dynamics in the real Ginzburg-Landau equation
• Validity and Limitation of the Newell‐Whitehead Equation
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