一类非线性演化方程的新多级准确解  

New multi-order exact solutions to a kind of nonlinear evolution equations

作　　者：付遵涛[1] 刘式适[1] 刘式达[1] 

机构地区：[1]北京大学物理学院,北京100871

出　　处：《物理学报》2003年第12期2949-2953,共5页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :40 175 0 16;40 0 45 0 16)资助的课题~~

摘　　要：在Lamé方程和新的Lamé函数的基础上 ,应用小扰动方法和Jacobi椭圆函数展开法求解一类非线性演化方程(如mKdV方程 ,非线性Klein Gordon方程Ⅱ等 ) ,获得多种新的多级准确解 .这些多级准确解对应着不同形式的周期波解 .这些解在极限条件下可以退化为多种形式的孤立波解 ,如带状孤立子、钟形孤立子等 .Based on the Lame equation and new Lame functions, the perturbation method and Jacobi elliptic function expansion method are applied to get the multi-order exact solutions of a kind of nonlinear evolution equations (such as mKdV equation, nonlinear Klein-Gordon equation II etc.), where some more new multi-order exact solutions are found among different nonlinear evolution equations. These multi-order exact solutions correspond to different periodic solutions, which can degenerate into different solitary wave solutions, such as band-soliton, bell-shaped solitary wave, etc.

关 键 词：非线性演化方程 多级准确解 JACOBI椭圆函数 数学物理方法 小扰动方法 Lame函数 孤立波解 周期波解 

分 类 号：O174[理学—数学]