The generalized tanh-coth method to special types of the fifth-order KdV equation

Abstract In this paper 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 KdV equation (fKdV). Three special cases that we consider here are the Caudrey–Dodd–Gibbon (CDG), the generalized Kaup–Kupershmidt (GKK) and the generalized Ito equations. New traveling wave solutions which include periodic and soliton solutions for three cases are formally derived.

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