Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices
Fu Jing-Li(傅景礼)a)†, Nie Ning-Ming(聂宁明)b), Huang Jian-Fei(黄健飞)c) Jimenez Salvadord), Tang Yi-Fa(唐贻发)b)e), Vazquez Luisf), and Zhao Wei-Jia(赵维加)c)
a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; c Department of Mathematics, Qingdao University, Qingdao 266071, China; d Departamento de Matemática Aplicada TTII, E. T. S. I. Telecomunicación, Universidad Politécnica de Madrid, 28040-Madrid, Spaine Departamento de Matemática Aplicada, Facultad de Matemáticas, Instituto de Matemática Interdisciplinar (IMI), Universidad Complutense de Madrid, 28040-Madrid, Spainf Departamento de Matemática Aplicada, Facultad de Informática, Instituto de Matemática Interdisciplinar (IMI), Universidad Complutense de Madrid, 28040-Madrid, Spain
Abstract This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange--Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.
Received: 26 September 2008
Revised: 04 December 2008
Accepted manuscript online:
Fund: Project supported
by the National Natural Science Foundation of China (Grants Nos
10672143 and 60575055) and State Key Laboratory of Scientific and
Engineering Computing, Chinese Academy of Sciences. Tang Yi-Fa
acknowledges the support under Sabbatical Program (SAB2006-0070) of
the Spanish Ministry of Education and Science. Jim\'enez S and
V\'azquez L acknowledge support of the Spanish
Ministry of Education and Science (Grant No MTM2005-05573).
Cite this article:
Fu Jing-Li(傅景礼), Nie Ning-Ming(聂宁明), Huang Jian-Fei(黄健飞) Jimenez Salvador, Tang Yi-Fa(唐贻发), Vazquez Luis, and Zhao Wei-Jia(赵维加) Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices 2009 Chin. Phys. B 18 2634
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