Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system

doi:10.1088/1674-1056/22/9/090201

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.

Keywords: symmetry invariant Ablowitz-Ladik-Lattice system wave equation

Received: 09 January 2013
Revised: 27 February 2013
Accepted manuscript online:

PACS:	02.20.-a	(Group theory)
	02.30.Ik	(Integrable systems)
	02.30.Ks	(Delay and functional equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 11272287).

Corresponding Authors: Fu Jing-Li
E-mail: sqfujingli@163.com

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Fu Jing-Li (傅景礼), Song Duan (宋端), Fu Hao (付昊), He Yu-Fang (何玉芳), Hong Fang-Yu (洪方昱) Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system 2013 Chin. Phys. B 22 090201

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Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system

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