Lie group theory was originally created more than 100 years ago as a tool for solving
ordinary and partial differential equations. In this article we review the results of a much …

Lie group theory started out as a theory of transformations of solutions of sets of differential
equations. 1–4 Over the years it has developed into a powerful tool for classifying differential …

The methods of Lie group analysis of differential equations are generalized so as to provide
an infinitesimal formalism for calculating symmetries of difference equations. Several …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

One of the difficulties encountered when studying physical theories in discrete space–time is
that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance) …

A sizable literature exists on discrete quantum mechanics, that is on quantum mechanics in
discrete space–time. We refer to a recent review for motivation and for an extensive list of …

Discrete heat equation with irregular thermal conductivity and tempered distributional data
Page 1 Proceedings of the Royal Society of Edinburgh, page 1 of 24 DOI:10.1017/prm.2023.84 …

Finite-difference analysis has recently attracted wide interest, both in mathematics and
physics. On the one hand, the advent of supercomputers and the development of efficient …

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 …

A method is presented for finding the Lie point symmetry transformations acting
simultaneously on difference equations and lattices, while leaving the solution set of the …