### 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 | |

Publication status | Published - Aug 2003 |

### Keywords

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

## Fingerprint Dive into the research topics of 'A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation'. Together they form a unique fingerprint.

## Cite this

Vakhnenko, V. O., Parkes, E. J., & Morrison, A. J. (2003). A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation.

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