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

Authors: Juncheng Wei and Matthias Winter
Journal: Proc. Amer. Math. Soc. 133 (2005), 1787-1796
MSC (2000): Primary 35B35, 76E30; Secondary 35B40, 76E06
Published electronically: November 19, 2004
MathSciNet review: 2120279
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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.

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Additional Information

Juncheng Wei
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

Matthias Winter
Affiliation: Fachbereich Mathematik, Universität Stuttgart, D-70511 Stuttgart, Germany

Keywords: Cubic-quintic Ginzburg-Landau equation, stability, pattern formation
Received by editor(s): November 5, 2002
Received by editor(s) in revised form: February 22, 2004
Published electronically: November 19, 2004
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society

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