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

Vakhnenko, V.O. and Parkes, E.J. and Morrison, A.J. (2003) A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos, Solitons and Fractals, 17 (4). pp. 683-692. ISSN 0960-0779 (http://dx.doi.org/10.1016/S0960-0779(02)00483-6)

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.

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• Item metadata

  Item type:	Article
  ID code:	82
  Dates:	Date Event August 2003 Published
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics Unknown Department
  Depositing user:	Miss Jacqueline Miller
  Date deposited:	21 Dec 2005
  Last modified:	11 Nov 2024 08:25
  Related URLs:	http://www.maths.strath.ac.uk/~caas35/vp...
  URI:	https://strathprints.strath.ac.uk/id/eprint/82