### Abstract

The N-soliton solution of a new nonlinear evolution equation, the modified generalised Vakhnenko equation, is found. 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 type decomposition. Different types of soliton are possible, namely loops, humps or cusps. Details of the different types of interactions between solitons are discussed in detail for the case N=2. A proof of the 'N-soliton condition' is given in Appendix A.

Original language | English |
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Pages (from-to) | 13-26 |

Number of pages | 13 |

Journal | Chaos, Solitons and Fractals |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2003 |

### Keywords

- n-soliton solution
- solitons
- Vakhnenko equation
- nonlinear equations

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## Cite this

Morrison, A. J., & Parkes, E. J. (2003). The N-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation).

*Chaos, Solitons and Fractals*,*16*(1), 13-26. https://doi.org/10.1016/S0960-0779(02)00314-4