Explicit solutions of the reduced Ostrovsky equation

E.J. Parkes

Research output: Contribution to journalArticle

45 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].
LanguageEnglish
Pages602-610
Number of pages8
JournalChaos, Solitons and Fractals
Volume31
Issue number3
DOIs
Publication statusPublished - Feb 2007

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Ostrovsky Equation
Explicit Solution
Matched Asymptotics
Solitary Waves
Traveling Wave Solutions
Traveling Wave
Wave equation
Approximate Solution
Exact Solution

Keywords

  • fractals
  • chaos theory
  • vakhnenko equation
  • physics

Cite this

Parkes, E.J. / Explicit solutions of the reduced Ostrovsky equation. In: Chaos, Solitons and Fractals. 2007 ; Vol. 31, No. 3. pp. 602-610.
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Explicit solutions of the reduced Ostrovsky equation. / Parkes, E.J.

In: Chaos, Solitons and Fractals, Vol. 31, No. 3, 02.2007, p. 602-610.

Research output: Contribution to journalArticle

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