Group classification of differential-difference equations: Low-dimensional Lie algebras

Abstract

Differential-difference equations of the form un = Fn(t, un−1, un, un+1, un−1, un, un+1) are classified according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry algebras. Here Fn is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t.