On a cubic-quintic Ginzburg-Landau equation with global coupling

Wei, Juncheng; Winter, Matthias

doi:10.1090/S0002-9939-04-07770-6

On a cubic-quintic Ginzburg-Landau equation with global coupling
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by Juncheng Wei and Matthias Winter PDF

Proc. Amer. Math. Soc. 133 (2005), 1787-1796 Request permission

Abstract:

We study standing wave solutions in a Ginzburg-Landau equation which consists of a cubic-quintic equation stabilized by global coupling \[ A_t= \Delta A +\mu A + c A^3 -A^5 -k A \left (\int _{R^n} A^2 dx\right ).\] We classify the existence and stability of all possible standing wave solutions.

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