Existence of standing waves for the complex Ginzburg–Landau equation

We study the existence of standing wave solutions of the complex Ginzburg–Landau equation(GL)φt−eiθ(ρI−Δ)φ−eiγ|φ|αφ=0 in RN, where α>0, (N−2)α0 and θ,γ∈R. We show that for any θ∈(−π/2,π/2) there exists ε>0 such that (GL) has a non-trivial standing wave solution if |γ−θ|−λ1, where λ1 is the fir...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-02, Vol.422 (1), p.579-593
Main Authors: Cipolatti, Rolci, Dickstein, Flávio, Puel, Jean-Pierre
Format: Article
Language:English
Subjects:
Complex Ginzburg–Landau equation
Standing waves
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Summary:We study the existence of standing wave solutions of the complex Ginzburg–Landau equation(GL)φt−eiθ(ρI−Δ)φ−eiγ|φ|αφ=0 in RN, where α>0, (N−2)α0 and θ,γ∈R. We show that for any θ∈(−π/2,π/2) there exists ε>0 such that (GL) has a non-trivial standing wave solution if |γ−θ|−λ1, where λ1 is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.08.057