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Multi-symplectic method for the generalized （2＋1）-dimensional KdV-mKdV equation

ISSN号：0567-7718
期刊名称：《力学学报：英文版》
时间：0
分类：O175.26[理学—数学;理学—基础数学] TV131.4[水利工程—水力学及河流动力学]
作者机构：[1]School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnincal University, 710072 Xi'an, China, [2]State Key Laboratory of Mechanical System & Vibration,Shanghai Jiao Tong University,200240 Shanghai, China, [3]State Key Laboratory of StructuralAnalysis of Industrial Equipment,Dalian University of Technology, 116023 Dalian, China
相关基金：The project was supported by the National Natural Science Foun- dation of China （11002115, 10972182, 11172239）, the Science Foundation of Aviation of China （2010ZB53021）, the China Post- doctoral Science Special Foundation （201003682）, 111 project （B07050） to the Northwestern Polytechnical University, the NPU Foundation for Fundamental Research （JC200938, JC20110259）, the Doctoral Program Foundation of Education Ministry of China （20106102110019）, the Open Foundation of State Key Laboratory of Mechanical System ＆ Vibration （MSV-2011-21） and the Open Foundation of State Key Laboratory of Structural Analysis of In- dustrial Equipment （GZ0802）.

作者： Wei-Peng Hu, Zi-Chen Deng, Yu-Yue Qin, Wen-Rong Zhang

关键词： Kdv-MKdv方程, Kdv-MKdv方程, 广义, PREISSMANN格式, Jacobi椭圆函数, 辛方法, 守恒定律, 周期波解, Generalized （2＋ 1）-dimensional KdV-mKdVequation Multi-symplectic Periodic wave solution Con-servation law ~ Jacobi elliptic function

中文摘要：

在现在的纸，包含三个任意的函数为的一个一般解决方案概括(2+1 ) 维的 KdV-mKdV 方程，它被导出从概括(1+1 ) 维的 KdV-mKdV 方程，首先借助于 Wiess 被介绍，小鼓， Carnevale (WTC ) 截断方法。然后有考虑的几条能量守恒定律的 multisymplectic 明确的表达被介绍为概括(2+1 ) 维的 KdV-mKdV 方程基于桥的 multisymplectic 理论。随后，源于以便以 Jacobi 椭圆形的功能的合理功能模仿周期的波浪答案一般答案，一个半含蓄的 multi-symplectic 计划被构造那等价于 Preissmann 计划。从数字实验的结果，我们能断定 multi-symplectic 计划能精确地模仿周期的波浪答案概括(2+1 ) 维的 KdV-mKdV 方程当时近似保存能量守恒定律。

英文摘要：

In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.

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