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Abundant exact and explicit solitary wave and periodic wave solutions to the Sharma-Tasso-Olver equation. (English) Zbl 1151.65076
Summary: This paper is concerned with a double nonlinear dispersive equation – the Sharma-Tasso-Olver equation. The extended hyperbolic function method is employed to investigate the solitary and periodic travelling waves in this equation. With the aid of Mathematica and the elimination method of W. J. Wu [Lect. Notes Comput. Sci. 834, 1–9 (1994; Zbl 0953.01500)], the abundant exact explicit solutions of the nonlinear Sharma-Tasso-Olver equation are derived. The solutions obtained in this paper include (a) solitary wave solutions, (b) the singular travelling wave solutions, and (c) periodic travelling wave solutions of triangle function types. Several entirely new exact solutions to the equation are explicitly obtained, in addition to deriving all known solutions in a systematic way. This work can be regarded as an extension to the recent work by A.-M. Wazwaz [Appl. Math. Comput. 188, No. 2, 1205–1213 (2007; Zbl 1118.65113)].
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q51Soliton-like equations