Parkes, E.J. (2007) *Explicit solutions of the reduced Ostrovsky equation.* Chaos, Solitons and Fractals, 31 (3). pp. 602-610. ISSN 0960-0779

## Abstract

It is shown that the Vakhnenko equation (VE) and the Ostrovsky-Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1-17].

Item type: | Article |
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ID code: | 3960 |

Keywords: | fractals, chaos theory, vakhnenko equation, physics, Mathematics, Physics |

Subjects: | Science > Mathematics Science > Physics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Dr Edward John Parkes |

Date Deposited: | 06 Aug 2007 |

Last modified: | 12 Mar 2012 10:40 |

URI: | http://strathprints.strath.ac.uk/id/eprint/3960 |

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