Ito方程组的对称分析与守恒律  

Symmetry analysis and conservation law of Ito equations

作　　者：张明霞 赵巧红 额尔敦布和[1,2] ZHANG Mingxia;ZHAO Qiaohong;EERDUN Buhe(School of Science,Inner Mongolian University of Technology,Hohhot 010051,China;Faculty of Mathematics and Big Data,Hohhot University for Nationalities,Hohhot 010051,China)

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与大数据学院,呼和浩特010051

出　　处：《内蒙古工业大学学报（自然科学版）》2023年第2期97-102,共6页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：国家自然科学基金项目(11661034);内蒙古自治区“草原英才”创新人才工程支持项目。

摘　　要：基于Lie群分析方法,得到了Ito方程组的一维子代数最优系统和相似约化系统,并借助Ibragimov的新守恒定理成功构造出该方程组的3个守恒律。结果表明:这些揭示了Ito方程组对称与守恒律之间的内在联系,而且克服了Nöether定理的局限性,对研究Ito方程组的相关属性方面具有重要意义。Based on the Lie group analysis method,a one-dimensional subalgebraic optimal system and a similar reduced system of Ito equations are obtained,and three conservation laws for the equations are successfully constructed with the help of Ibragimov's new conservation theorem.The results show the intrinsic connection between the symmetry and conservation laws of the system of Ito equations,and overcome the limitation of Nöether's theorem,which is important for studying the relevant properties of the system of Ito equations.

关 键 词：Ito方程组 LIE对称 相似约化 新守恒定理 守恒律 

分 类 号：O175.2[理学—数学]