The symmetries of wave equations on new lattices

doi:10.1088/1674-1056/19/6/060301

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.

Keywords: new lattice equation symmetry discrete wave equation invariant

Received: 30 August 2009
Accepted manuscript online:

PACS:	05.50.+q	(Lattice theory and statistics)
	02.10.Ud	(Linear algebra)

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10672143).

Cite this article:

He Yu-Fang(何玉芳), Fu Jing-Li(傅景礼), and Li Xiao-Wei(李晓伟) The symmetries of wave equations on new lattices 2010 Chin. Phys. B 19 060301

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