Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 014, 7 pages      nlin.SI/0602001      http://dx.doi.org/10.3842/SIGMA.2006.014

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

Faruk Güngör
Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, 34469, Istanbul, Turkey

Received November 30, 2005, in final form January 20, 2006; Published online January 30, 2006

Abstract
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.

Key words: Kadomtsev-Petviashvili and Davey-Stewartson equations; symmetry group; Virasoro algebra.

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