Double Traveling Wave Solutions of the Coupled Nonlinear Klein-Gordon Equations and the Coupled Schr\"{o}dinger-Boussinesq Equation |
Received:February 20, 2017 Revised:September 01, 2017 |
Key Words:
the new multiple $( \frac{G'}{G})$-expansion the coupled nonlinear Klein-Gordon equations the coupled Schr\"{o}dinger-Boussinesq equation double traveling wave solutions
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Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11202106; 61201444), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20123228120005), the Jiangsu Information and Communication Engineering Preponderant Discipline Platform, the Natural Science Foundation of Jiangsu Province (Grant No.BK20131005), the Jiangsu Qing Lan Project and the Natural Sciences Fundation of the Universities of Jiangsu Province (Grant No.13KJB170016) and the Fundamental Research Funds for the Southeast University (Grant No.CDLS-2016-03). |
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Abstract: |
The new multiple $(\frac{G'}{G})$-expansion method is proposed in this paper to seek the exact double traveling wave solutions of nonlinear partial differential equations. With the aid of symbolic computation, this new method is applied to construct double traveling wave solutions of the coupled nonlinear Klein-Gordon equations and the coupled Schr\"{o}dinger-Boussinesq equation. As a result, abundant double traveling wave solutions including double hyperbolic tangent function solutions, double tangent function solutions, double rational solutions, and a series of complexiton solutions of these two equations are obtained via this new method. The new multiple $( \frac{G'}{G})$-expansion method not only gets new exact solutions of equations directly and effectively, but also expands the scope of the solution. This new method has a very wide range of application for the study of nonlinear partial differential equations. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2017.06.005 |
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