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Zbl 1100.35099
Vernov, Sergey Yu.
Painlevé analysis and exact solutions of nonintegrable systems. (English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2--10, 2005. Sofia: Bulgarian Academy of Sciences. 280-291 (2006). ISBN 954-8495-30-9/pbk

Summary: We consider the cubic complex Ginzburg-Landau equation. Applying Hone's method, based on the use of the Laurent series solutions and the residue theorem, we prove that this equation has no elliptic standing wave solutions. This result supplements Hone's, result, that this equation has no elliptic travelling wave solutions. It is shown that Hone's method can be applied to a system of polynomial differential equations more effectively than to an equivalent differential equation.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
37K20 Relations with algebraic geometry, etc.
30B50 Series expansions (one complex variable)

Keywords: cubic complex Ginzburg-Landau equation; Laurent series; elliptic standing wave solutions

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