非线性强度KG型方程精确解和多重Compacton解  

Exact solutions and multi-Compacton solutions of nonlinear intensity KG type equation

作　　者：田立新[1] 于水猛[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2005年第3期227-230,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10071003)

摘　　要：引进非线性强度概念,研究了非线性强度Klein-Gordon型方程.改进广义投射Riccati方程方法,给出了非线性偏微分方程的解的表达式,运用此方法得到非线性强度Klein-Gordon型方程的Kink解、周期波解等丰富精确解.通过拟设法求得该方程的单重、双重及多重Compacton解,给出了非线性色散强度、非线性耗散强度与非线性强度影响不同关系下解的具体变化形式.证明了非线性色散强度、非线性耗散强度与非线性强度影响的共同作用导致非线性强度KleinGordon型方程的本质变化.Nonlinear intensity Klein-Gordon-type equation is studied by introducing the concept of ~nonli- near intensity. The generalized projective Riccati equation method is improved. By applying this method, Kink solutions, periodic solutions and abundant exact solutions are obtained. By using ansatzes, Compacton solutions and multi-Compacton solutions are obtained. The solution forms under different relations of nonlinear dispersive intensity, nonlinear dissipative intensity and nonlinear intensity effect are given. It is proved that the above factors lead to an essential change of nonlinear intensity Klein-Gordon-type ~equation.

关 键 词：非线性偏微分方程 非线性强度Klein—Gordon型方程 广义投射Riccati方程方法 孤立波解 COMPACTON解 

分 类 号：O175[理学—数学]