中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/19/6/060301

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The symmetries of wave equations on new lattices

李晓伟1, 何玉芳2, 傅景礼2   

  1. (1)Department of Physics, Shangqiu Teacher College, Shangqiu 476000, China; (2)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
  • 收稿日期:2009-08-30 出版日期:2010-06-15 发布日期:2010-06-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.~10672143).

The symmetries of wave equations on new lattices

He Yu-Fang(何玉芳)a), Fu Jing-Li(傅景礼)a)†, and Li Xiao-Wei(李晓伟)b)   

  1. a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Department of Physics, Shangqiu Teacher College, Shangqiu 476000, China
  • Received:2009-08-30 Online:2010-06-15 Published:2010-06-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.~10672143).

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摘要： This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.

Abstract: This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.

Key words: new lattice equation, symmetry, discrete wave equation, invariant

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
02.10.Ud (Linear algebra)