On the Virasoro Structure of Symmetry Algebras of Nonlinear Partial Differential Equations

Faruk Güngör

Symmetry, integrability and geometry: methods and applications, Tome 2 (2006)

Résumé

We discuss Lie algebras of the Lie symmetry groups of two generically non-integrable equations in one temporal and two space dimensions arising in different contexts. The first is a generalization of the KP equation and contains 9 arbitrary functions of one and two arguments. The second one is a system of PDEs that depend on some physical parameters. We require that these PDEs are invariant under a Kac–Moody–Virasoro algebra. This leads to several limitations on the coefficients (either functions or parameters) under which equations are prime candidates for being integrable.

Détail

Keywords: Kadomtsev–Petviashvili and Davey–Stewartson equations; symmetry group; Virasoro algebra.

Bibliographie

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