Vakhnenko, V.O. and Parkes, E.J.
(2012)
*Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation.*
Progress of Theoretical Physics, 127 (4).
pp. 593-613.

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## Abstract

In this paper the inverse scattering method is applied to the Vakhnenko-Parkes equation. We describe a procedure for using the inverse scattering transform to find the solutions that are associated with both the bound state spectrum and continuous spectrum of the spectral problem. The suggested special form of the singularity function gives rise to the multi-mode periodic solutions. Sufficient conditions are obtained in order that the solutions become real functions. The interaction of the solitons and multi-mode periodic waves is studied. The procedure is illustrated by considering a number of examples.

Item type: | Article |
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ID code: | 39586 |

Keywords: | inverse scattering, Vakhnenko-Parkes equation, discrete spectrum, continuous spectrum, Probabilities. Mathematical statistics, Physics and Astronomy (miscellaneous) |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 08 May 2012 08:59 |

Last modified: | 26 Mar 2015 16:41 |

URI: | http://strathprints.strath.ac.uk/id/eprint/39586 |

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