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 solutions and the residue theorem, we have proved 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 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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. https://projecteuclid.org/euclid.pgiq/1436909362.