利用一类混合方法构造摄动方程的近似孤子解(英文)  

Construction of Approximate Soliton Solutions for the Perturbed Equations by a Hybrid Approach

作　　者：额尔敦布和[1,2] 特木尔朝鲁[3] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]呼和浩特民族学院数学系,呼和浩特010051 [3]上海海事大学文理学院,上海200135

出　　处：《内蒙古工业大学学报（自然科学版）》2011年第4期447-454,共8页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：Supported by Nationl Natural Science Foundation of China(No.11071159);the College Science Research Project of Inner Mongolia(No.NJzy08180)

摘　　要：基于近似对称群方法和一类一般变系数Riccati方程展开法,提出构造摄方程近似孤子解的一类混合方法.然后,选择一种摄动KdV方程举例说明该方法,得到其凶括近似周期和近似孤立波解的四个近似孤子解.该方法可适用于数学物理中的其它摄动方程.Based on the approximate symmetry group method and a generalized Riccati equation with variable coefficients expansion method,a hybrid approach is proposed to construct the approximate soliton solutions of the perturbed differential equations.Then,a perturbed KdV equation is chosen to illustrate the method.As a result,four new soliton solutions,which include approximate periodic solutions and approximate solitary wave solutions are obtained.This method can be used to the other perturbed equations in mathematical physics.

关 键 词：近似对称方法 Riccati方程方法 摄动方程 近似周期解 近似孤立波解 

分 类 号：O152.5[理学—数学] O411[理学—基础数学]