Dispersionless Davey-Stewartson system: Lie symmetry algebra, symmetry group and exact solutions

Abstract

Lie symmetry algebra of the dispersionless Davey-Stewartson (dDS) system is shown to be infinite-dimensional. The structure of the algebra turns out to be Kac-Moody-Virasoro one when the system is of type dDS-I. For the type dDS-II system this rare structure is spoilt. Symmetry group transformations are constructed using a global approach. They are split into both connected and discrete ones. Several exact solutions are obtained as an application of the symmetry properties.