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On stationary solutions of the reduced Ostrovsky equation: Periodic waves, compactons and compound solitons

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  • Stepanyants, Y.A.

Abstract

Detailed analysis of solitary and periodic stationary solutions of the reduced Ostrovsky equation is presented. The full Ostrovsky equation (ut+c0ux+αuux+βuxxx)x=γu was derived in 1978 for oceanic waves affected by Earth rotation, and its reduced form without small-scale dispersion, (ut+c0ux+αuux)x=γu, was pointed out in his original paper and then, derived later by many authors in different physical contexts. However, some aspects of stationary solutions to the last equation remained unclear so far. An attempt to introduce clarity to this problem is undertaken in this paper.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:193-204
    DOI: 10.1016/j.chaos.2005.05.020
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    Cited by:

    1. Abrashkin, Anatoly, 2019. "Unsteady Gerstner waves," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 152-158.
    2. Parkes, E.J., 2007. "Explicit solutions of the reduced Ostrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 602-610.

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