The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method

V.O. Vakhnenko, E.J. Parkes

Research output: Contribution to journalArticlepeer-review

98 Citations (Scopus)

Abstract

A Bäcklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse scattering method has a third-order eigenvalue problem. A procedure for finding the exact N-soliton solution of the Vakhnenko equation via the inverse scattering method is described. The procedure is illustrated by considering the cases N=1 and N=2.
Original languageEnglish
Pages (from-to)1819-1826
Number of pages7
JournalChaos, Solitons and Fractals
Volume13
Issue number9
DOIs
Publication statusPublished - Jul 2002

Keywords

  • multi-soliton solutions
  • Vakhnenko equation
  • inverse scattering
  • numerical analysis

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