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Explicit solutions of the reduced Ostrovsky equation

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  • Parkes, E.J.

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].

Suggested Citation

  • Parkes, E.J., 2007. "Explicit solutions of the reduced Ostrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 602-610.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:3:p:602-610
    DOI: 10.1016/j.chaos.2005.10.028
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    References listed on IDEAS

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    1. Stepanyants, Y.A., 2006. "On stationary solutions of the reduced Ostrovsky equation: Periodic waves, compactons and compound solitons," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 193-204.
    2. Boyd, John P., 2005. "The cnoidal wave/corner wave/breaking wave scenario: A one-sided infinite-dimension bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(3), pages 235-242.
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    Cited by:

    1. Parkes, E.J., 2008. "Some periodic and solitary travelling-wave solutions of the short-pulse equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 154-159.

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