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Sine-cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation. (English) Zbl 1151.35418
Summary: We use a modified form of the sine-cosine method for obtaining exact soliton solutions of the generalized fifth-order nonlinear evolution equation. An analysis of this method is presented. The present method shows that the solutions involve either sec$^{2}$ or sech$^{2}$ under certain conditions. General forms of those conditions are determined for the first time. Exact solutions for special cases of this problem such as the Sawada-Kotera and Lax equations are found.

35Q53KdV-like (Korteweg-de Vries) equations
35G20General theory of nonlinear higher-order PDE
Full Text: DOI
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