Discrete derivatives and symmetries of difference equations

Abstract

We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation.

submitted to J.Phys. A 10 Latex pages

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• Integrable maps from Galois differential algebras, Borel transforms and number sequences
• The stabilizer group of honeycomb lattices and its application to deformed monolayers
• Canonical Transformations in Crystals