# The N-soliton solution of a generalized Vakhnenko equation

Morrison, A.J. and Parkes, E.J.
(2001)
*The N-soliton solution of a generalized Vakhnenko equation.*
Glasgow Mathematical Journal, 43 (A).
pp. 65-90.
ISSN 0017-0895

## Abstract

The N-soliton solution of a generalised Vakhnenko equation is found, where N is an arbitrary positive integer. The solution, which is obtained by using a blend of transformations of the independent variables and Hirota's method, is expressed in terms of a Moloney and Hodnett (1989) type decomposition. Different types of soliton are possible, namely loops, humps or cusps. Details of the different types of interactions between solitons, including resonant soliton interactions, are discussed in detail for the case N=2. A proof of the 'N-soliton condition' is given in the Appendix.

Item type: | Article |
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ID code: | 2023 |

Keywords: | N-soliton, Vakhnenko equation, Hirota's method, Mathematics, Mathematics(all) |

Subjects: | Science > Mathematics |

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

Depositing user: | Strathprints Administrator |

Date Deposited: | 26 Nov 2006 |

Last modified: | 29 Apr 2016 00:07 |

Related URLs: | |

URI: | http://strathprints.strath.ac.uk/id/eprint/2023 |