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

Vakhnenko, V.O. and Parkes, E.J. (2002) The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method. Chaos, Solitons and Fractals, 13 (9). pp. 1819-1826. ISSN 0960-0779 (http://dx.doi.org/10.1016/S0960-0779(01)00200-4)

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.

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• Item metadata

  Item type:	Article
  ID code:	79
  Dates:	Date Event July 2002 Published
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Miss Jacqueline Miller
  Date deposited:	19 Dec 2005
  Last modified:	11 Nov 2024 08:22
  Related URLs:	http://www.maths.strath.ac.uk/~caas35/v&...
  URI:	https://strathprints.strath.ac.uk/id/eprint/79