Proceedings of the International Conference on Geometry, Integrability and Quantization

Construction of Elliptic Solutions to the Quintic Complex One-Dimensional Ginzburg–Landau Equation

Sergey Yu Vernov

Abstract

The Conte–Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg–Landau equation (CGLE5) allows us to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions to the CGLE5.

Article information

Source
Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2007), 322-333

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436792839

Digital Object Identifier
doi:10.7546/giq-8-2007-322-333

Mathematical Reviews number (MathSciNet)
MR2341213

Zentralblatt MATH identifier
1221.35407

Citation

Vernov, Sergey Yu. Construction of Elliptic Solutions to the Quintic Complex One-Dimensional Ginzburg–Landau Equation. Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, 322--333, Softex, Sofia, Bulgaria, 2007. doi:10.7546/giq-8-2007-322-333. https://projecteuclid.org/euclid.pgiq/1436792839


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