
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 nonintegrable 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 KacMoodyVirasoro algebra. This leads to several
limitations on the coefficients (either functions or parameters)
under which equations are prime candidates for being integrable.
Key words:
KadomtsevPetviashvili and DaveyStewartson equations; symmetry group; Virasoro algebra.
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