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 具任意次非线性项的广义修正DGH方程的求解与稳定性研究(PDF)

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

期数:
2017年03期
页码:
240-247
栏目:
研究论文
出版日期:
2017-05-15

文章信息/Info

Title:
 Research on the Stability and Solving Solutions of the General Revised Nonlinear DGH Equation with Arbitrary Order
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DGH方程Bcklund变换稳定性
Keywords:
 first integralgeneralized modified Dullin-Gottwald-Holm equationBcklund transformationstability
分类号:
-
DOI:
-
文献标识码:
A
摘要:
 通过几个步骤,获得了具任意次非线性项的广义修正的Dullin-Gottwald-Holm(DGH)方程的几种新结论.步骤一,给出了两种非线性常微分方程的拟Bcklund变换.步骤二,利用函数变换,将具任意次非线性项的广义修正的DGH方程的求解问题转化为常微分方程组的求解问题.步骤三,通过常微分方程组的首次积分,构造了具任意次非线性项的广义修正的DGH方程的无穷序列新解.步骤四,用符号计算系统Maple分析了广义修正的DGH方程的相轨线的稳定性.通过几个步骤,获得了具任意次非线性项的广义修正的Dullin-Gottwald-Holm(DGH)方程的几种新结论.步骤一,给出了两种非线性常微分方程的拟Bcklund变换.步骤二,利用函数变换,将具任意次非线性项的广义修正的DGH方程的求解问题转化为常微分方程组的求解问题.步骤三,通过常微分方程组的首次积分,构造了具任意次非线性项的广义修正的DGH方程的无穷序列新解.步骤四,用符号计算系统Maple分析了广义修正的DGH方程的相轨线的稳定性.
Abstract:
 By some steps,some kinds of new conclusions of the generalized modified Dullin-Gottwald-Holm (DGH) equation with arbitrary order are obtained.Step 1,the quasi Bcklund transformations of two kinds of nonlinear ordinary differential equations are presented.Step 2,with the help of function transformation,the problem of solving the solutions of the generalized modified DGH equation with arbitrary order is changed to the problem of solving the solutions of ordinary differential equations.Step 3,by the first integral of ordinary differential equations,the new infinite sequence solutions of the generalized modified DGH equation with arbitrary order are constructed.Step 4,by symbol computational system Maple,the stability of the phase trajectory of the generalized modified DGH equation is analysed.

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备注/Memo

备注/Memo:
 收稿日期:2017-03-25
基金项目:国家自然科学基金(11361040);内蒙古自治区自然科学基金(2015MS0128);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古自治区2016年硕士研究生科研创新项目(S20161013502)和内蒙古师范大学研究生科研创新基金项目(CXJJS16081)资助
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.主要从事复杂系统的稳定与控制研究.E-mail:573028703@qq.com
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