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arXiv · 1407.4043

Lie-point symmetries of the discrete Liouville equation

Decio Levi·Luigi Martina·Pavel Winternitz
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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 $ SL_x \lf 2 , \mathbb{R} \rg \otimes SL_y \lf 2 , \mathbb{R} \rg $. The invariant scheme is an explicit one and provides a much better approximation of exact solutions than comparable standard (non invariant) schemes.

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Decio Levi, Luigi Martina, Pavel Winternitz. 2014-07-15. Lie-point symmetries of the discrete Liouville equation. https://doi.org/10.1088/1751-8113/48/2/025204

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