Proceedings of the International Conference on Geometry, Integrability and Quantization
- Geom. Integrability & Quantization
- Proceedings of the Seventh International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2006) , 280 - 291
Painlevé Analysis and Exact Solutions of Nonintegrable Systems
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.
First available in Project Euclid: 14 July 2015
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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.