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arXiv · 1404.6461

Existence of standing waves for the complex Ginzburg-Landau equation

R. Cipolatti·F. Dickstein·J. P Puel
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Abstract

We prove the existence of non-trivial standing wave solutions of the complex Ginzburg-Landau equation $ϕ_t - e^{iθ}(ρI- Δ) φ- e^{iγ} |ϕ|^αφ=0 $ in $\Rn$, where $(N-2)α<4$, $θ,γ\in (-π/2,π/2)$ and $ρ>0$. Analogous result is obtained in a ball $Ω\in\Rn$ for $ρ>-λ_1$, where $λ_1$ is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions.

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R. Cipolatti, F. Dickstein, J. P Puel. 2014-04-25. Existence of standing waves for the complex Ginzburg-Landau equation. https://arxiv.org/abs/1404.6461

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