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

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

中国物理B ›› 2013, Vol. 22 ›› Issue (9): 90201-090201.doi: 10.1088/1674-1056/22/9/090201

• GENERAL • 下一篇

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

傅景礼^a, 宋端^b, 付昊^c, 何玉芳^a, 洪方昱^a

a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;
b Department of Physics, Eastern Liaoning University, Dandong 118001, China;
c China Jingye Engineering Corporation Limited, Shenzhen Brach, Shenzhen 518054, China

收稿日期:2013-01-09 修回日期:2013-02-27 出版日期:2013-07-26 发布日期:2013-07-26
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 11272287).

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

Fu Jing-Li (傅景礼)^a, Song Duan (宋端)^b, Fu Hao (付昊)^c, He Yu-Fang (何玉芳)^a, Hong Fang-Yu (洪方昱)^a

a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;
b Department of Physics, Eastern Liaoning University, Dandong 118001, China;
c China Jingye Engineering Corporation Limited, Shenzhen Brach, Shenzhen 518054, China

Received:2013-01-09 Revised:2013-02-27 Online:2013-07-26 Published:2013-07-26
Contact: Fu Jing-Li E-mail:sqfujingli@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 11272287).

摘要/Abstract

摘要： 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.

关键词: symmetry, invariant, Ablowitz-Ladik-Lattice system, wave equation

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.

Key words: symmetry, invariant, Ablowitz-Ladik-Lattice system, wave equation

中图分类号: (Group theory)

02.20.-a

02.30.Ik (Integrable systems) 02.30.Ks (Delay and functional equations)

傅景礼, 宋端, 付昊, 何玉芳, 洪方昱. Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system[J]. 中国物理B, 2013, 22(9): 90201-090201.

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[J]. Chin. Phys. B, 2013, 22(9): 90201-090201.

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

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

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