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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

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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
ID code: 2023
Keywords: N-soliton, Vakhnenko equation, Hirota's method, Mathematics, Mathematics(all)
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Unknown Department
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Depositing user: Strathprints Administrator
Date Deposited: 26 Nov 2006
Last modified: 04 Sep 2014 10:41
URI: http://strathprints.strath.ac.uk/id/eprint/2023

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