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 Word: the new multiple $( \frac{G'}{G})$-expansion   the coupled nonlinear Klein-Gordon equations   the coupled Schr\"{o}dinger-Boussinesq equation   double traveling wave solutions  
Fund ProjectL: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).
Author NameAffiliation
Lanfang SHI College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Jiangsu 210044, P. R. China 
Ziwen NIE College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Jiangsu 210044, P. R. China; Ministry of Education Key Laboratory of Child Development and Learning Science, Southeast University, Jiangsu 210096, P. R. China 
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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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