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

摘要

We discuss Lie algebras of the Lie symmetry groups of two genericallynon-integrable equations in one temporal and two space dimensions arising indifferent contexts. The first is a generalization of the KP equation andcontains 9 arbitrary functions of one and two arguments. The second one is asystem of PDEs that depend on some physical parameters. We require that thesePDEs are invariant under a Kac-Moody-Virasoro algebra. This leads to severallimitations on the coefficients (either functions or parameters) under whichequations are prime candidates for being integrable.