Noether Theorems and Discrete Variational Integrators in Field Theory |

Li-Li Xia
^{a,b}, Li-Qun Chen^{a,c,d} and Chang-Xin Liu^{ b}^{a}Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
^{b}Department of Physics, Henan Institute of Education, Zhengzhou 450046, China
^{c}Department of Mechanics, Shanghai University, Shanghai 200444, China
^{d}Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China |

Received: May 1, 2014; In final form: January 31, 2015 |

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The discrete analogue of the Noether-type identities in field theory is investigated by means of the difference discrete variational principle in which the difference is regarded as an entire geometric object. The discrete counterparts of the Noether theorems are obtained. It is proved that there exists the discrete version of the Noether conservation law in field theory. The discretization for the nonlinear SchrÃ¶dinger equation is presented to illustrate the results. |

DOI: 10.12693/APhysPolA.127.669 PACS numbers: 02.20.Sv, 11.30.-j |