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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

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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.