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

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.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Cited by in corpus (2)

• Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy
• Analysis of the symmetry group and exact solutions of the dispersionless KP equation in $n+1$ dimensions