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On a cubic-quintic Ginzburg-Landau equation with global coupling
Authors:Juncheng Wei  Matthias Winter
Institution:Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong ; Fachbereich Mathematik, Universität Stuttgart, D-70511 Stuttgart, Germany
Abstract:We study standing wave solutions in a Ginzburg-Landau equation which consists of a cubic-quintic equation stabilized by global coupling

\begin{displaymath}A_t= \Delta A +\mu A + c A^3 -A^5 -k A \left(\int_{R^n} A^2\,dx\right).\end{displaymath}

We classify the existence and stability of all possible standing wave solutions.

Keywords:Cubic-quintic Ginzburg-Landau equation  stability  pattern formation
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