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arXiv · 1010.3324

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

Wen-Xiu Ma·Tingwen Huang·Yi Zhang
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Abstract

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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Wen-Xiu Ma, Tingwen Huang, Yi Zhang. 2010-10-16. A multiple exp-function method for nonlinear differential equations and its application. https://doi.org/10.1088/0031-8949%2F82%2F06%2F065003

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