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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.

MSC:

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