Proceedings of the International Conference on Geometry, Integrability and Quantization

Painlevé Analysis and Exact Solutions of Nonintegrable Systems

Sergey Yu. Vernov

Abstract

Here we consider the cubic complex Ginzburg–Landau equation. Applying the Hone’s method, based on the use of the Laurent-series solu- tions and the residue theorem, we have proved that this equation has no el- liptic standing wave solutions. This result supplements Hone’s result, that this equation has no elliptic travelling wave solutions. It has been shown that the Hone’s method can be applied to a system of polynomial differential equations more effectively than to an equivalent differential equation.

Article information

Source
Proceedings of the Seventh International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2006) , 280-291

Dates
First available in Project Euclid: 14 July 2015

Permanent link to this document
http://projecteuclid.org/ euclid.pgiq/1436909362

Digital Object Identifier
doi:10.7546/giq-7-2006-280-291

Mathematical Reviews number (MathSciNet)
MR2228379

Zentralblatt MATH identifier
1100.35099

Citation

Vernov, Sergey Yu. Painlevé Analysis and Exact Solutions of Nonintegrable Systems. Proceedings of the Seventh International Conference on Geometry, Integrability and Quantization, 280--291, Softex, Sofia, Bulgaria, 2006. doi:10.7546/giq-7-2006-280-291. http://projecteuclid.org/euclid.pgiq/1436909362.


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