期刊文献+

常规三阶常微分方程在对称群作用下的可积性 被引量:1

Integrable properties of three order ordinary differential equations under the action of the symmetry group
收藏 分享 导出
摘要 针对常规三阶微分方程的可积性,采用一种不同于降阶、消元的新方法,利用对称群理论,采用将三阶常微分方程作用在Lie群上的方法,通过一个变换将方程组的任意解映成该方程组的另一个解,求出Lie群生成元,得到首次积分,进而分析微分方程的可积性.研究结果表明:常规三阶微分方程在对称群作用下不可积,同时也将研究对象从二阶微分方程拓展到三阶微分方程. In view of the problem of integrable property of ordinary differential equations, a new method is adopted, which is different from the method that reduced order and elimination. In this paper, the method of using three order ordinary differential equation action on Lie group used the theory of symmetric group. By means of a transformation, the solution of the equation is transformed into another solution of the equation in order to find out Lie group generating element and get the first integral. On this basis, this paper analyzes the problem of integrable property of differential equation. The results of the study show that the three order differential equations are not integrable under the action of the symmetric group, and at the same time, the research object is extended from the second order differential equation to the three order differential equation.
作者 孙丹阳 盖如栋 SUN Danyang1, GAI Rufong2 ( 1. College of Science, Liaoning Technical University, Fuxin 123000, China; 2. College of Science, Huaiyin Institute of Technology, Huaiyin 223300, China)
出处 《辽宁工程技术大学学报:自然科学版》 CAS 北大核心 2017年第2期206-209,共4页 Journal of Liaoning Technical University (Natural Science Edition)
基金 国家自然科学基金项目(61074188)
关键词 三阶常微分方程 LIE群 对称群 可积性 首次积分 three order ordinary differential equation Lie group symmetric group integrable property first integrals
作者简介 孙丹阳(1990-),女,辽宁大石桥人,硕士研究生,主要从事系统控制理论与应用的研究.
  • 相关文献

参考文献9

二级参考文献81

共引文献2

引证文献1

投稿分析

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部 意见反馈