Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices |
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Authors: | Fu Jing-Li Nie Ning-Ming Huang Jian-Fei Jimé nez Salvador Tang Yi-Fa Vá zquez Luis Zhao Wei-Jia |
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Affiliation: | ([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,Spain; [e] Departamento de Matemática Aplicada,Facultad de Matemáticas,Instituto de Matemática Interdisciplinar (IMI), Universidad Complutense de Madrid, 28040-Madrid, Spain; [f] Departamento de Matemátic Aplicada,Facultad de Informática,Instituto de Matemática Interdisciplinar (IMI), Universidad Complutense de Madrid, 28040-Madrid, Spain) |
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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. Thisapproach 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. |
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Keywords: | Lagrange--Maxwell equation Lie point symmetry discrete mechanico-electrical system conserved quantity |
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