The new multiple (G'/G)-expansion method and its application to the coupled nonlinear Klein–Gordon equations and the coupled Schr?dinger–Boussinesq equation
Received:February 20, 2017  Revised:August 31, 2017
Key Word: the new multiple -expansion   the coupled nonlinear Klein–Gordon equations   the coupled Schr?dinger–Boussinesq equation    double traveling wave solutions  
Fund ProjectL:The National Natural Science Foundation of China(No.11202106,No.61201444), The Specialized Research Fund for the Doctoral Program of Higher Education (No.20123228120005), The Jiangsu Information and Communication Engineering Preponderant Discipline Platform, The Natural Science Foundation of Jiangsu Province(No.BK20131005), The Jiangsu Qing Lan Project and the Natural Sciences Fundation of the Universities of Jiangsu Province (No.13KJB170016)
Author NameAffiliationE-mail
Langfang SHI College of Mathematics and Statistics,Nanjing University of Information Science and Technology shilf108@163.com 
Ziwen NIE College of Mathematics and Statistics,Nanjing University of Information Science and Technology niezw109@163.com 
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Abstract:
      The new multiple -expansion method is firstly 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?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 -expansion method not only get new exact solutions of equations directly and effectively, but also expand the scope of the solution. This new method has a very wide range of application for the study of nonlinear partial differential equations.
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