| 非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的双行波解 |
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| 引用本文： | 史兰芳,聂子文.非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的双行波解[J].数学研究及应用,2017,37(6):679-696. |
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| 作者姓名： | 史兰芳 聂子文 |
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| 作者单位： | 南京信息工程大学数学与统计学院, 江苏 南京 210044,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 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11202106; 61201444),教育部高等学校博士学科点专项科研基金(Grant No.20123228120005),江苏省“信息与通信工程”优势学科建设基金,江苏省自然科学基金(Grant No.BK20131005),江苏省青蓝工程和江苏省高校自然科学研究基金(Grant No.13KJB170016),东南大学基本科研业务费资助项目(Grant No.CDLS-2016-03). |
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| 摘 要： | 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.
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| 关 键 词： | 全新复合$(\frac{G''}{G})$展开法 非线性Klein-Gordon方程组 耦合Schr\"{o}dinger-Boussinesq方程组 双行波解 |
| 收稿时间： | 2017/2/20 0:00:00 |
| 修稿时间： | 2017/9/1 0:00:00 |
Double Traveling Wave Solutions of the Coupled Nonlinear Klein-Gordon Equations and the Coupled Schr\"{o}dinger-Boussinesq Equation |
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| Lanfang SHI and Ziwen NIE.Double Traveling Wave Solutions of the Coupled Nonlinear Klein-Gordon Equations and the Coupled Schr\"{o}dinger-Boussinesq Equation[J].Journal of Mathematical Research with Applications,2017,37(6):679-696. |
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| Authors: | Lanfang SHI and Ziwen NIE |
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| Institution: | College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Jiangsu 210044, P. R. China and 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. |
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| Keywords: | 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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