广义修正的DGH方程的奇点分类与求解问题研究  

Classification of Singularity and Study on Solving of the Generalized Modified DGH Equation

作　　者：伊丽娜[1] 包俊东[1] 套格图桑[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2016年第1期14-22,共9页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(批准号:11361040);内蒙古自治区高等学校科学研究基金(批准号:NJZY12031);内蒙古自治区自然科学基金(批准号:2015MS0128)资助的课题

摘　　要：利用辅助方程与函数变换相结合的方法,通过几个步骤研究了广义修正的Dullin-Gottwald-Holm方程的稳定性与求解问题.步骤一,通过两种函数变换,把广义修正的Dullin-Gottwald-Holm方程化为常微分方程组.步骤二,利用常微分方程组的首次积分,分析了广义修正的Dullin-Gottwald-Holm方程的稳定性与奇点分类问题.步骤三,用首次积分将广义修正的Dullin-Gottwald-Holm方程的求解问题化为常微分方程的求解问题.步骤四,利用常微分方程的Bcklund变换等相关结论,构造了广义修正的Dullin-Gottwald-Holm方程的无穷序列类孤子新解.A method for combing the auxiliary equation with the function transformation is pres- ented to research the stability and solving of the generalized modified DGH equation by the follow- ing steps. Step 1,two kinds of function transformations are applied to change the generalized modi- fied DGH equation into a set of ordinary differential equations. Step 2,the first integral of the ordi- nary differential equations are presented to analyze the stability and the classification of singularity of the generalized modified DGH equation. Step 3,according to the first integral, the solving of the generalized modified DGH equation is transformed into the solving of ordinary differential equa- tions. Step 4, Baicklund transformation of ordinary differential equations and relative conclusions are introduced to construct the new infinite sequence soliton-like solutions of the generalized modified DGH equation.

关 键 词：首次积分 广义修正的Dullin-Gottwald-Holm方程 稳定性与奇点分类 无穷序列新解 

分 类 号：O175.29[理学—数学]