### Abstract

The N-soliton solution of a generalised Vakhnenko equation is found, where N is an arbitrary positive integer. The solution, which is obtained by using a blend of transformations of the independent variables and Hirota's method, is expressed in terms of a Moloney and Hodnett (1989) type decomposition. Different types of soliton are possible, namely loops, humps or cusps. Details of the different types of interactions between solitons, including resonant soliton interactions, are discussed in detail for the case N=2. A proof of the 'N-soliton condition' is given in the Appendix.

Original language | English |
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Pages (from-to) | 65-90 |

Number of pages | 25 |

Journal | Glasgow Mathematical Journal |

Volume | 43 |

Issue number | A |

DOIs | |

Publication status | Published - Jun 2001 |

### Keywords

- N-soliton
- Vakhnenko equation
- Hirota's method

## Cite this

Morrison, A. J., & Parkes, E. J. (2001). The N-soliton solution of a generalized Vakhnenko equation.

*Glasgow Mathematical Journal*,*43*(A), 65-90. https://doi.org/10.1017/S0017089501000076