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Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method. (English) Zbl 1107.65092
Summary: We use the tanh method for solving several forms of the fifth-order nonlinear Korteweg-de Vries (KdV) equation. The forms include those of P. D. Lax [Commun. Pure Appl. Math. 21, 467–490 (1968; Zbl 0162.41103)], K. Sawada and T. Kotera [Prog. Theor. Phys. 51, 1355–1367 (1974; Zbl 1125.35400)], D. Kaup [Stud. Appl. Math. 62, 189–216 (1980; Zbl 0431.35073)], B. A. Kupershmidt [A super KdV equation: an integrable system, Phys. Lett. 102A, 213–215 (1984)], M. Ito [J. Phys. Soc. Jpn. 49, 771–778 (1980)], and other related special cases. Abundant solitons solutions are derived. Two necessary criteria are established to build up reliable strategies that govern the relation between the parameters of the equation. Previously known solutions are recovered and entirely new bell shaped solitons are determined.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations