A multiple exp-function method for nonlinear differential equations and its application

Details A multiple exp-function method for nonlinear differential equations and its application A multiple exp-function method for nonlinear differential equations and its application

2010-10-16

arxiv.org/abs/1010.3324v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 16 figures

Scientific paper

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.

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