A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation

V.O. Vakhnenko, E.J. Parkes, A.J. Morrison

Research output: Contribution to journalArticle

155 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)683-692
Number of pages9
JournalChaos, Solitons and Fractals
Volume17
Issue number4
DOIs
Publication statusPublished - Aug 2003

Keywords

  • Bäcklund transformation
  • Vakhnenko equation
  • solitons
  • nonlinear equations
  • inverse scattering

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