Noether Theorems and Discrete Variational Integrators in Field Theory
Li-Li Xiaa,b, Li-Qun Chena,c,d and Chang-Xin Liu b
aShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
bDepartment of Physics, Henan Institute of Education, Zhengzhou 450046, China
cDepartment of Mechanics, Shanghai University, Shanghai 200444, China
dShanghai 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 Schrödinger equation is presented to illustrate the results.

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