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The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations. (English) Zbl 1115.65106
Summary: The extended tanh method is used to derive new solitons solutions for several forms of the fifth-order nonlinear Korteweg-de Vries (KdV) equation. The forms include the Lax, Sawada-Kotera, Sawada-Kotera-Parker-Dye, Kaup-Kupershmidt, Kaup-Kupershmidt-Parker-Dye, and the Ito equations. The criteria established by the author [ibid. 182, No. 1, 283–300 (2006; Zbl 1107.65092)] to build up reliable relations between the parameters of the equation are confirmed by using this new approach. Entirely new bell shaped solitons are determined.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
Full Text: DOI
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