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

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

2006-01-31

arxiv.org/abs/nlin/0602001v1

SIGMA 2 (2006), 014, 7 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.3842/SIGMA.2006.014

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.

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