Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system |
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Authors: | Fu Jing-Li Song Duan Fu Hao He Yu-Fang and Hong Fang-Yu |
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Affiliation: | [1]Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China [2]Department of Physics, Eastern Liaoning University, Dandong 118001, China [3]China Jingye Engineering Corporation Limited, Shenzhen Brach, Shenzhen 518054, China |
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Abstract: | In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified. |
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Keywords: | symmetry invariant Ablowitz-Ladik-Lattice system wave equation |
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