Vakhnenko, V.O. and Parkes, E.J. and Morrison, A.J. (2003) *A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation.* Chaos, Solitons and Fractals, 17 (4). pp. 683-692. ISSN 0960-0779

Official URL: http://dx.doi.org/10.1016/S0960-0779(02)00483-6

## Abstract

A Bäcklund transformation both in bilinear and in ordinary form for the transformed generalised Vakhnenko equation (GVE) is derived. It is shown that the equation has an infinite sequence of conservation laws. An inverse scattering problem is formulated; it has a third-order eigenvalue problem. A procedure for finding the exact N-soliton solution to the GVE via the inverse scattering method is described. The procedure is illustrated by considering the cases N=1 and 2.

Item type: | Article |
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ID code: | 82 |

Keywords: | Bäcklund transformation, Vakhnenko equation, solitons, nonlinear equations, inverse scattering, Mathematics, Mathematics(all) |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics Unknown Department |

Related URLs: | |

Depositing user: | Miss Jacqueline Miller |

Date Deposited: | 21 Dec 2005 |

Last modified: | 04 Sep 2014 12:00 |

URI: | http://strathprints.strath.ac.uk/id/eprint/82 |

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