Standing waves of the complex Ginzburg–Landau equation

We prove the existence of nontrivial standing wave solutions of the complex Ginzburg–Landau equation ϕt=eiθΔϕ+eiγ|ϕ|αϕ+kϕ on a bounded domain with Dirichlet boundary conditions. Our result requires that α>0 be sufficiently small.

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Bibliographic Details
Published in:Nonlinear analysis 2014-07, Vol.103, p.26-32
Main Authors: Cazenave, Thierry, Dickstein, Flávio, Weissler, Fred B.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Boundary conditions
Complex Ginzburg–Landau equation
Dirichlet problem
Mathematical analysis
Mathematics
Nonlinearity
Standing waves
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Summary:We prove the existence of nontrivial standing wave solutions of the complex Ginzburg–Landau equation ϕt=eiθΔϕ+eiγ|ϕ|αϕ+kϕ on a bounded domain with Dirichlet boundary conditions. Our result requires that α>0 be sufficiently small.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2014.03.001