巢湖学院学报2006，Vol.8Issue(3)：46-52,7.
The Invariance of the Differential Equations and Conserved Quantities
The Invariance of the Differential Equations and Conserved Quantities
摘要
Abstract
In this paper , a new form conserved quantity of differential equations is presented. The conserved quantity is constructed only based on the general Lie group of transformation vector of the differential equations. The first-order and second-order differential equations are studied, respectively. Two theorems concerning conservedquantities are proved. The relations between these theorems and preious conservation laws are discussed. A condition is given to exclude trivial conserved quantities. Finally, we give two examples to illustrate the application of the results.关键词
differential equation/Lie symmetry/infinitesimal generator/conserved quantityKey words
differential equation/Lie symmetry/infinitesimal generator/conserved quantity分类
数理科学引用本文复制引用
Zhang Hong-bin,Chen Li-qun,Liu Rong-wan..The Invariance of the Differential Equations and Conserved Quantities[J].巢湖学院学报,2006,8(3):46-52,7.基金项目
Project supported by the National Natural Science Foundation of China under Grant No. 10172056 and the Science Research of the Education Bureau of Anhui Province under Grant No. 2006kj263. （）
