Periodic and solitary-wave solutions of an extended reduced Ostrovsky equation

E. John Parkes

Research output: Contribution to journalArticle

Abstract

Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves.
LanguageEnglish
Number of pages17
JournalSymmetry, Integrability and Geometry: Methods and Applications
Volume4
Issue number053
Publication statusPublished - 2008

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Ostrovsky Equation
Periodic Wave Solution
Solitary Wave Solution
Periodic Wave
Compact Support
Solitary Waves
Traveling Wave Solutions

Keywords

  • Ostrovsky equation
  • Ostrovsky–Hunter equation
  • Vakhnenko equation
  • periodic waves
  • solitary waves
  • corner waves
  • cuspons
  • loops

Cite this

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abstract = "Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves.",
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Periodic and solitary-wave solutions of an extended reduced Ostrovsky equation. / Parkes, E. John.

In: Symmetry, Integrability and Geometry: Methods and Applications, Vol. 4, No. 053, 2008.

Research output: Contribution to journalArticle

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KW - Ostrovsky equation

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KW - cuspons

KW - loops

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