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Explicit solutions of the reduced Ostrovsky equation. (English) Zbl 1138.35399
Summary: 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 analytic periodic and solitary travelling-wave solutions of the OHE are derived by using a method exploited 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 {\it J. P. Boyd} [Eur. J. Appl. Math. 16, No. 1, 65--81 (2005; Zbl 1079.35087)].

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
35B10Periodic solutions of PDE
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References:
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