Pulses in a complex Ginzburg-Landau system: Persistence under coupling with slow diffusion

DOI10.1016/j.physd.2007.05.009zbMath1158.34032OpenAlexW2038445964MaRDI QIDQ2643349

Nienke Valkhoff, Geertje Hek

Publication date: 23 August 2007

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2007.05.009

zbMATH Keywords

homoclinic orbitpulse solutioncoupled Ginzburg-Landau equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

A remark on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg–Landau equation

Cites Work

• Breaking the hidden symmetry in the Ginzburg-Landau equation
• Geometric singular perturbation theory for ordinary differential equations
• Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
• Stabilization by slow diffusion in a real Ginzburg-Landau system
• Solitary waves under the influence of a long-wave mode
• Large stable pulse solutions in reaction-diffusion equations
• A stability index analysis of 1-D patterns of the Gray-Scott model
• Oscillatory pattern formation with a conserved quantity
• The world of the complex Ginzburg-Landau equation
• Nonlinear dynamics of sand banks and sand waves
• Pattern formation with a conservation law
• Existence and stability of singular patterns in a Ginzburg Landau equation coupled with a mean field
• Algebraically decaying pulses in a Ginzburg–Landau system with a neutrally stable mode
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