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The N-soliton solution of a generalised Vakhnenko equation

Published online by Cambridge University Press:  25 July 2002

A. J. Morrison  and
E. J. Parkes
A. J. Morrison
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK e-mail: ta.amor@maths.strath.ac.uk and ejp@maths.strath.ac.uk
E. J. Parkes
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK e-mail: ta.amor@maths.strath.ac.uk and ejp@maths.strath.ac.uk
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Abstract

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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 & 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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue A , June 2001 , pp. 65 - 90
Copyright
© 2001 Glasgow Mathematical Journal Trust