Sine-Gordon方程的多辛Leap-frog格式  

Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation

作　　者：张宇[1] 邓子辰[1,2] 胡伟鹏[1] 

机构地区：[1]西北工业大学力学与土木建筑学院,西安710072 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《应用数学和力学》2013年第5期437-444,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11172239;11002115);111引智计划基金资助项目(B07050);高校博士点基金资助项目(20126102110023);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目(GZ0802)

摘　　要：非线性发展方程由于具有多种形式的解析解而吸引着众多的研究者,借助多辛保结构理论研究了Sine-Gordon方程的多辛算法.利用Hamilton变分原理,构造出了Sine-Gordon方程的多辛格式;采用显辛离散方法得到了leap-frog多辛离散格式,该格式满足多辛守恒律;数值结果表明leap-frog多辛离散格式能够精确地模拟Sine-Gordon方程的孤子解和周期解,模拟结果证实了该离散格式具有良好的数值稳定性.The nonlinear wave equation, which possesses various forms of analytical solutions, was investigated widely in last several decades. The multi-symplectic method for the Sine-Gor-don equation in Hamilton space was proposed. Based on Hamiltonian variational principle, the multi-symplectic formulations of the Sine-Gordon equation were deduced, and then, the leap- frog multi-symplectic discretization scheme was constructed using explicit symplectic discrete method. The numerical results for the Sine-Gordon equation illustrate that the leap-frog multi-symplectic scheme can simulate the propagation of the soliton and the periodic solution for the Sine-Gordon equation accurately, which show the superiority of the multi-symplectic algorithm when dealing with nonlinear evolution equations.

关 键 词：保结构 多辛方法 Sine—Gordon方程 leap—frog格式 

分 类 号：O175.24[理学—数学]