Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Abstract

Classification of differential-difference equation of the form ${\ddot{u}}_{nm}=F_{nm}(t,\{u_{pq}\}{|}_{(p,q)\in \Gamma })$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.

24 pages, 1 figure

References in corpus (5)

• Continuous Symmetries of Difference Equations
• Lie point symmetries of difference equations and lattices
• Lie symmetries of multidimensional difference equations
• Symmetry classification of KdV-type nonlinear evolution equations
• Symmetry Classification of Diatomic Molecular Chains

Cited by in corpus (1)

• Symmetries, conservation laws and Noether's theorem for differential-difference equations