Adomian分解法在完全非线性S-G方程中的运用  

Application of Adomian decomposition method to fully nonlinear S-G equation

作　　者：王玉春[1] 

机构地区：[1]宿迁学院,江苏宿迁223800

出　　处：《成都信息工程学院学报》2009年第1期91-98,共8页Journal of Chengdu University of Information Technology

摘　　要：为分析具有高非线性强度下的偏微分方程的初值问题,简化变量分离等方法带来的繁杂计算,研究了一类完全非线性Sine-Gordon方程以及它的近似方程(在|up|很小的情况下),经过适当的函数变换,运用改进的Ado-mian分解法解决了一些特殊情况下它们的初值问题,结合Talyor级数展开式,得到了一些精确解:扭结解(kink)、紧孤子解(compacton)、多重紧孤子解、compacton-kink解。另外运用线性化的方法结合不同形式的解得到它们一些更加丰富的新形式的精确解。In order to study the initial problem of the partial differential equations with high nonlinear intensity and simplify the complicated calculation of the variable-separation method a type of fully nonlinear Sine-Gordon equations and the approximate Sine-Gordon equation(under the condition that |up| is very small) are studied.By using a proper function transformation some initial problems of many equations with special nonlinear terms are solved by the Adomian decomposition method and some exact solution suc...

关 键 词：完全非线性Sine-Gordon方程 近似S-G方程 改进的Adomian分解法 ADOMIAN多项式 COMPACTON解 

分 类 号：O175.8[理学—数学]