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, which is typical for integrable evolution equations in $$2+1$$ dimensions. Symmetry group transformations are constructed using a direct (global) approach. They are split into both connected and discrete ones. Several exact solutions are obtained as an application of the symmetry properties.