|本期目录/Table of Contents|

广义修正的DGH方程的奇点分类与求解问题研究(PDF)

《内蒙古大学学报(自然科学版)》[ISSN:1000-9035/CN:22-1262/O4]

期数:
2016年01期
页码:
14-22
栏目:
研究论文
出版日期:
2016-01-30

文章信息/Info

Title:
Classification of Singularity and Study on Solving of the Generalized Modified DGH Equation
作者:
伊丽娜包俊东套格图桑
内蒙古师范大学数学科学学院,呼和浩特 010022
Author(s):
YI Li-naBAO Jun-dongTaogetusang
College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China
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
Keywords:
the first integralthe generalized modified DullinGottwaldHolm equationstability and the classification of singularitynew infinite sequence soliton solution
分类号:
O175.29
DOI:
-
文献标识码:
A
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.
Abstract:
A method for combing the auxiliary equation with the function transformation is presented to research the stability and solving of the generalized modified DGH equation by the following steps.Step 1,two kinds of function transformations are applied to change the generalized modified DGH equation into a set of ordinary differential equations.Step 2,the first integral of the ordinary 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 equations.Step 4,Bcklund 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.

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备注/Memo

备注/Memo:
收稿日期:2015-10-25
基金项目: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)和内蒙古自治区自然科学基金(批准号:2015MS0128)资助的课题
作者简介:伊丽娜(1991-),女(蒙古族),内蒙古通辽人,2015级硕士研究生.研究方向:复杂系统的稳定与控制,非线性偏微分方程理论.E-mail:573028703@qq.com.
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