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

V.O. Vakhnenko; E.J. Parkes; A.J. Morrison

doi:10.1016/S0960-0779(02)00483-6

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

V.O. Vakhnenko, E.J. Parkes, A.J. Morrison

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

213 Citations (Scopus)

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.

Original language	English
Pages (from-to)	683-692
Number of pages	9
Journal	Chaos, Solitons and Fractals
Volume	17
Issue number	4
DOIs	https://doi.org/10.1016/S0960-0779(02)00483-6
Publication status	Published - Aug 2003

Keywords

Bäcklund transformation
Vakhnenko equation
solitons
nonlinear equations
inverse scattering

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10.1016/S0960-0779(02)00483-6

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abstract = "A B{\"a}cklund 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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AU - Vakhnenko, V.O.

AU - Parkes, E.J.

AU - Morrison, A.J.

PY - 2003/8

Y1 - 2003/8

N2 - 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.

AB - 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.

KW - Bäcklund transformation

KW - Vakhnenko equation

KW - solitons

KW - nonlinear equations

KW - inverse scattering

UR - http://www.maths.strath.ac.uk/~caas35/vp&mCSF03.pdf

UR - http://dx.doi.org/10.1016/S0960-0779(02)00483-6

U2 - 10.1016/S0960-0779(02)00483-6

DO - 10.1016/S0960-0779(02)00483-6

M3 - Article

SN - 0960-0779

VL - 17

SP - 683

EP - 692

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 4

ER -

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

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Keywords

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