Existence of standing waves for the complex Ginzburg-Landau equation

R. Cipolatti, F. Dickstein, J. P Puel

We prove the existence of non-trivial standing wave solutions of the complex Ginzburg-Landau equation ${\varphi }_t-e^{i\theta }(\rho I-\Delta )\phi -e^{i\gamma }|\varphi {|}^{\alpha }\phi =0$ in $\Rn$, where $(N-2)\alpha <4$, $θ,γ\in…