## Abstract

The procedure for finding the solutions of the Vakhnenko-Parkes equation by means

of the inverse scattering method is described. The continuous spectrum is taken into

account in the associated eigenvalue problem. The suggested special form of the

singularity function for continuous part of the spectral data gives rise to the multimode solutions. The sufficient conditions are proved in order that these solutions become real functions. The interaction of the N periodic waves is studied. The procedure is illustrated by considering a number of examples

of the inverse scattering method is described. The continuous spectrum is taken into

account in the associated eigenvalue problem. The suggested special form of the

singularity function for continuous part of the spectral data gives rise to the multimode solutions. The sufficient conditions are proved in order that these solutions become real functions. The interaction of the N periodic waves is studied. The procedure is illustrated by considering a number of examples

Original language | English |
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Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 53 |

Issue number | 6 |

Early online date | 11 Jun 2012 |

DOIs | |

Publication status | Published - 2012 |

## Keywords

- eigenvalue problem
- nonlinear equations
- Vakhnenko-Parkes equation