Lie-point symmetries of the discrete Liouville equation
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Bibliographic record
Abstract
The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries. We do however construct a difference system approximating the Liouville equation that is invariant under the maximal finite subalgebra SLx (2,R) ⊗ SLy (2,R). The invariant scheme is an explicit one and provides a much better approximation of exact solutions than comparable standard (non invariant) schemes. 1
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