Hone, Andrew N.W.
(2005)
*
Non-existence of elliptic travelling wave solutions of the complex Ginzburg-Landau equation.
*
Physica D: Nonlinear Phenomena,
205
(1-4).
pp. 292-306.
ISSN 0167-2789.
(doi:10.1016/j.physd.2004.10.011)
(The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
(KAR id:680)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |

Official URL http://dx.doi.org/10.1016/j.physd.2004.10.011 |

## Abstract

We give a simple proof that, for generic parameter values, the cubic complex one-dimensional Ginzburg-Landau equation has no elliptic travelling wave solutions. This is contrary to the expectations of Musette and Conte, in Physica D 181 (2003) 70-79, that elliptic solutions of zero codimension should exist. The method of proof, based on the residue theorem, is very general, and can be applied to determine necessary conditions for the existence of elliptic travelling waves for any autonomous partial differential equation. As another application, we prove that Kudryashov's codimension-one elliptic solution of the generalized Kuramoto-Sivashinsky equation is the only one possible. (c) 2005 Elsevier B.V. All rights reserved.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1016/j.physd.2004.10.011 |

Uncontrolled keywords: | travelling waves; complex one-dimensional Ginzburg-Landau equation; elliptic functions; residue theorem |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Andrew Hone |

Date Deposited: | 19 Dec 2007 18:25 UTC |

Last Modified: | 16 Nov 2021 09:39 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/680 (The current URI for this page, for reference purposes) |

Hone, Andrew N.W.: | https://orcid.org/0000-0001-9780-7369 |

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