Explicit solutions of the reduced Ostrovsky equation

E.J. Parkes

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47 Citations (Scopus)

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].
Original languageEnglish
Pages (from-to)602-610
Number of pages8
JournalChaos, Solitons and Fractals
Volume31
Issue number3
DOIs
Publication statusPublished - Feb 2007

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Keywords

  • fractals
  • chaos theory
  • vakhnenko equation
  • physics

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