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The generalized tanh-coth method to special types of the fifth-order KdV equation. (English) Zbl 1154.65364
Summary: We use a generalization of the well-known tanh-coth method to obtain new periodic and soliton solutions for several forms of the fifth-order Korteweg-de Vries equation (fKdV). Three special cases that we consider here are the Caudrey-Dodd-Gibbon (CDG) [P. J. Caudrey, R. K. Dodd and J. D. Gibbon, Proc. R. Soc. Lond., Ser. A 351, 407–422 (1976; Zbl 0346.35024)], the generalized Kaup-Kupershmidt (GKK) [D. J. Kaup, Stud. Appl. Math. 62, 189–216 (1980; Zbl 0431.35073)] and the generalized Ito equations. New traveling wave solutions which include periodic and soliton solutions for three cases are formally derived.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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