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.


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