The N-soliton solution of a generalized Vakhnenko equation

A.J. Morrison, E.J. Parkes

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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.
Original languageEnglish
Pages (from-to)65-90
Number of pages25
JournalGlasgow Mathematical Journal
Volume43
Issue numberA
DOIs
Publication statusPublished - Jun 2001

Keywords

  • N-soliton
  • Vakhnenko equation
  • Hirota's method

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