Bessel方程的对称性和守恒量  

Symmetries and Conserved Quantities of Bessel Equation

作　　者：姜文安[1] 孙鹏 谷家扬[1] 夏丽莉[2] 

机构地区：[1]江苏科技大学船舶与海洋工程学院,江苏镇江212003 [2]北京工业大学机电学院,北京100124

出　　处：《江西科学》2018年第1期1-6,共6页Jiangxi Science

基　　金：国家自然科学基金项目(11702119;51779109;11502071);江苏省自然科学基金项目(BK20170565)

摘　　要：研究了经典Bessel方程的Lagrange化。基于Darboux方法,建立了Bessel方程的Lagrange方程。通过研究Bessel方程的Noether对称性、Lie对称性、Mei对称性和共形不变性来寻求守恒量。利用相应对称性的定义和确定方程,得到了5种守恒量。研究n阶经典Bessel方程来说明本文方法的有效性。This paper explores a novel Lagrange formulations of classical Bessel equation. Based onthe method of Darboux, Lagrange formulation of Bessel equation is established. The Noether symmetry, Lie symmetry, Mei symmetry and conformal invariance of Bessel equation is devoted to find conserved quantity. The definitions and determining equations of corresponding symmetries are employed, and five types of conserved quantities are obtained. nth order classical Bessel equation arestudied to show the effectiveness of the proposed method.

关 键 词：BESSEL方程 Lagrange化 对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]