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扩充偏微分方程(组)守恒律和对称的辅助方程方法及微分形式吴方法的应用
引用本文:特木尔朝鲁,额尔敦布和,郑丽霞.扩充偏微分方程(组)守恒律和对称的辅助方程方法及微分形式吴方法的应用[J].应用数学学报,2007,30(5):910-927.
作者姓名:特木尔朝鲁  额尔敦布和  郑丽霞
作者单位:1. 上海海事大学数学系,上海,200135;内蒙古工业大学理学院,呼和浩特,010051
2. 内蒙古工业大学理学院,呼和浩特,010051
基金项目:国家自然科学基金;内蒙古自然科学基金;内蒙古高等学校科研项目
摘    要:首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性.

关 键 词:偏微分方程  守恒律  对称  变分  吴方法
修稿时间:2006-10-26

Auxiliary Equation(s) Method to Determine Extended Conservation Laws and Symmetries for A Partial Differential Equation(s) and Applications of Differential Form Wu's method
TEMUERCHAOLU,EERDUNBUHE,ZHENG LIXIA.Auxiliary Equation(s) Method to Determine Extended Conservation Laws and Symmetries for A Partial Differential Equation(s) and Applications of Differential Form Wu''''s method[J].Acta Mathematicae Applicatae Sinica,2007,30(5):910-927.
Authors:TEMUERCHAOLU  EERDUNBUHE  ZHENG LIXIA
Institution:1.Department of Mathematics of Shanghai Maritime University, Shanghai 200135;2.College of Sciences of Inner Mongolia University of Technology, Huhhot 010051
Abstract:Firstly, using strategy of introducing associated auxiliary equation(s) to a given partial differential equation(s) without admitting Lagrangian, we make the extended equations possess a variational principle. Based on this, the concepts of extended conservation law and extended symmetry to given partial differential equation(s) are put forwarded. Secondly, A computational method to produce extended conservation laws and extended symmetries to given partial differential equation(s) are suggested. Thirdly, an algorithm to determine original conservation laws of general form partial differential equation(s) is given. Fourthly, in our methods the differential form Wu's method is used to solve the system of determining equations for conservation laws and symmetries of given equation(s). Finally, as applications of our methods given in this paper, new (extended) conservation laws and symmetries for five evolution equations included nonlinear Telegraph equations are determined.
Keywords:partial differential equation(s)  conservation law  symmetry  variational principle  Wu's method
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