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

V.O. Vakhnenko; E.J. Parkes

doi:10.1016/S0960-0779(01)00200-4

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

V.O. Vakhnenko, E.J. Parkes

Mathematics And Statistics

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117 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 language	English
Pages (from-to)	1819-1826
Number of pages	7
Journal	Chaos, Solitons and Fractals
Volume	13
Issue number	9
DOIs	https://doi.org/10.1016/S0960-0779(01)00200-4
Publication status	Published - Jul 2002

Keywords

multi-soliton solutions
Vakhnenko equation
inverse scattering
numerical analysis

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10.1016/S0960-0779(01)00200-4

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abstract = "A B{\"a}cklund 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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T1 - The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method

AU - Vakhnenko, V.O.

AU - Parkes, E.J.

PY - 2002/7

Y1 - 2002/7

N2 - 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.

AB - 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.

KW - multi-soliton solutions

KW - Vakhnenko equation

KW - inverse scattering

KW - numerical analysis

UR - http://www.maths.strath.ac.uk/~caas35/v&pCSF02.pdf

UR - http://dx.doi.org/10.1016/S0960-0779(01)00200-4

U2 - 10.1016/S0960-0779(01)00200-4

DO - 10.1016/S0960-0779(01)00200-4

M3 - Article

SN - 0960-0779

VL - 13

SP - 1819

EP - 1826

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 9

ER -

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

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Keywords

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