Double Traveling Wave Solutions of the Coupled Nonlinear Klein-Gordon Equations and the Coupled Schr\"{o}dinger-Boussinesq Equation

DOI：10.3770/j.issn:2095-2651.2017.06.005

 作者 单位 史兰芳 南京信息工程大学数学与统计学院, 江苏 南京 210044 聂子文 南京信息工程大学数学与统计学院, 江苏 南京 210044 东南大学儿童发展与学习科学教育部重点实验室, 江苏 南京 210096

本文提出了一种全新复合$(\frac{G'}{G})$展开方法,运用这种新方法并借助符号计算软件构造了非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的多种双行波解,包括双双曲正切函数解,双正切函数解,双有理函数解以及它们的混合解. 复合$(\frac{G'}{G})$展开方法不但直接有效地求出了两类非线性偏微分方程的双行波解,而且扩大了解的范围.这种新方法对于研究非线性偏微分方程具有广泛的应用意义.

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.