### Abstract

Language | English |
---|---|

Pages | 683-692 |

Number of pages | 9 |

Journal | Chaos, Solitons and Fractals |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2003 |

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### Keywords

- Bäcklund transformation
- Vakhnenko equation
- solitons
- nonlinear equations
- inverse scattering

### Cite this

*Chaos, Solitons and Fractals*,

*17*(4), 683-692. https://doi.org/10.1016/S0960-0779(02)00483-6

}

*Chaos, Solitons and Fractals*, vol. 17, no. 4, pp. 683-692. https://doi.org/10.1016/S0960-0779(02)00483-6

**A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation.** / Vakhnenko, V.O.; Parkes, E.J.; Morrison, A.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation

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

VL - 17

SP - 683

EP - 692

JO - Chaos, Solitons and Fractals

T2 - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 4

ER -