Pulses in a complex Ginzburg-Landau system: Persistence under coupling with slow diffusion
type: Item
instance of: scholarly article
title: Pulses in a complex Ginzburg-Landau system: Persistence under coupling with slow diffusion
zbMATH Open document ID: 1158.34032
author: Nienke Valkhoff
author: Geertje Hek
published in: Physica D
publication date: 2007-08-23T00:00:00Z
review text: The article studies existence and persistence of traveling pulse solutions for a complex Ginzburg-Landau equation coupled to a diffusion equation that acts on a long spatial scale (slow diffusion). The authors choose a model that forms a connection between two limiting systems of a very different nature: the diffusion equation is coupled with a real Ginzburg-Landau system on one hand (having dissipative dynamics), when the coefficients have small imaginary parts, and with a nonlinear Schrödinger equation on the other hand (which is Hamiltonian, integrable and with infinitely many conservation laws). In both cases existence and persistence results are proved, using analytical, partly asymptotic and geometric methods.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 5182408
zbMATH Keywords: coupled Ginzburg-Landau equation
zbMATH Keywords: pulse solution
zbMATH Keywords: homoclinic orbit
reviewed by: Gabriela Liţcanu
MaRDI profile type: Publication
full work available at URL: j.physd.2007.05.009
OpenAlex ID: W2038445964
cites work: The world of the complex Ginzburg-Landau equation
cites work: Breaking the hidden symmetry in the Ginzburg-Landau equation
cites work: Large stable pulse solutions in reaction-diffusion equations
cites work: A stability index analysis of 1-D patterns of the Gray-Scott model
cites work: Stabilization by slow diffusion in a real Ginzburg-Landau system
cites work: Algebraically decaying pulses in a Ginzburg–Landau system with a neutrally stable mode
cites work: Geometric singular perturbation theory for ordinary differential equations
cites work: Q3374503
cites work: Q4847945
cites work: Q4703405
cites work: Nonlinear dynamics of sand banks and sand waves
cites work: Pattern formation with a conservation law
cites work: Q4550347
cites work: Existence and stability of singular patterns in a Ginzburg Landau equation coupled with a mean field
cites work: Solitary waves under the influence of a long-wave mode
cites work: Q4952434
cites work: Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
cites work: Oscillatory pattern formation with a conserved quantity
DOI: 10.1016/J.PHYSD.2007.05.009
description: scientific article