Lie symmetries of multidimensional difference equations

Abstract

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be used to perform symmetry reduction. The method generalizes one presented in a recent publication for the case of ordinary difference equations. In turn, it can easily be generalized to difference systems involving an arbitrary number of dependent and independent variables.

References in corpus (2)

• Lie point symmetries of difference equations and lattices
• Symmetry Classification of Diatomic Molecular Chains

Cited by in corpus (16)

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• Discretization of partial differential equations preserving their physical symmetries
• Lie Symmetries and Exact Solutions of First Order Difference Schemes
• Lie Point Symmetries and Commuting Flows for Equations on Lattices
• Symmetry preserving discretization of ordinary differential equations. Large symmetry groups and higher order equations
• The Korteweg-de Vries equation and its symmetry-preserving discretization
• Lie discrete symmetries of lattice equations
• Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
• Symmetries of differential-difference dynamical systems in a two-dimensional lattice
• Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations
• The Jacobi last multiplier for difference equations