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Mei symmetries and conserved quantities for non-conservative Hamiltonian difference systems with irregular lattices

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Abstract

Noether conserved quantities and Mei symmetries for non-conservative Hamiltonian difference systems with irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie point transformations acting on the lattice, as well as the difference equations, and the determining equations of Mei symmetries are obtained for the systems. The discrete versions of Noether conserved quantity are constructed by the Mei symmetries. An example is presented to illustrate the results.

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Acknowledgements

This work was supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209), the National Natural Science Foundation of China (Grant No. 11102060), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20093108110005), and the program for Shanghai Leading Academic Discipline Project (Grant No. S30106).

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Authors and Affiliations

  1. Department of Physics, Henan Institute of Education, Zhengzhou, 450046, China

    Li-Li Xia

  2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Li-Li Xia & Li-Qun Chen

  3. Department of Mechanics, Shanghai University, Shanghai, 200444, China

    Li-Qun Chen

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  1. Li-Li Xia
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  2. Li-Qun Chen
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Correspondence to Li-Qun Chen.

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Xia, LL., Chen, LQ. Mei symmetries and conserved quantities for non-conservative Hamiltonian difference systems with irregular lattices. Nonlinear Dyn 70, 1223–1230 (2012). https://doi.org/10.1007/s11071-012-0526-8

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  • DOI: https://doi.org/10.1007/s11071-012-0526-8

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