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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.

MSC:
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)
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