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

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

2009-03-20

arxiv.org/abs/0903.3576v2

Physics

Mathematical Physics

24 pages, 1 figure

Scientific paper

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ 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.

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