(2+1)-维Calogero-Bogoyavlenskii-Schiff方程的对称约化及其新的类孤子解  

Symmetry reduction and some new soliton-like solutions of (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation

作　　者：智红燕[1] 

机构地区：[1]中国石油大学数学与计算科学学院,山东东营257061

出　　处：《中国石油大学学报（自然科学版）》2010年第3期170-173,共4页Journal of China University of Petroleum(Edition of Natural Science)

基　　金：中国石油大学(华东)博士科研启动项目(Y080808);中央高校基本科研业务费专项资金(09CX05004A)

摘　　要：借助于符号计算软件Maple,首先利用古典Lie群法给出(2+1)-维Calogero-Bogoyavlenskii-Schiff(CBS)方程的无穷维对称变换群,并以此为基础约化该方程,得到低维的微分方程,并利用改进的直接法给出CBS方程的新显式解与旧解之间的关系进而得到方程的部分新的类孤子解。这些解有助于研究某些复杂的物理现象,及验证数值求解法则的可行性。Based on the symbolic computation system-Maple,the infinite-dimensional symmetry group of transformation was presented using the classical Lie group method.And based on the symmetry group,the symmetry reduction was derived for（2＋1）-dimensional Calogero-Bogoyavlenskii-Schiff（CBS）equation.Then,with an improved direct method,the relationship between the new explicit solutions and the old ones of the CBS equation was presented and some new soliton-like solutions of the CBS equation were obtained.The obtained solutions maybe provide a useful help for physicists to study more complicated physical phenomena and for mathematicians to check on the accuracy and reliability of numerical algorithm.

关 键 词：Calogero-Bogoyavlenskii-Schiff方程 古典Lie群法 直接法 对称约化 不变解 

分 类 号：O175.24[理学—数学]