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A multiple exp-function method for nonlinear differential equations and its application. (English) Zbl 1219.35209

Summary: A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota’s perturbation scheme. With the help of Maple, applying the approach to the \((3+1)\)-dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit one-wave, two-wave and three-wave solutions, which include one-soliton, two-soliton and three-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of the two-wave and three-wave solutions.

MSC:

35Q51 Soliton equations
35C08 Soliton solutions
35A22 Transform methods (e.g., integral transforms) applied to PDEs

Software:

Maple
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