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

TL;DR

This paper analyzes the infinite-dimensional Lie symmetry algebra of the dispersionless Davey-Stewartson system, revealing its Kac-Moody-Virasoro structure, and constructs symmetry transformations to derive exact solutions.

Contribution

It identifies the Lie symmetry algebra of the dispersionless Davey-Stewartson system as Kac-Moody-Virasoro and constructs symmetry group transformations for solution generation.

Findings

The symmetry algebra is infinite-dimensional and Kac-Moody-Virasoro in structure.

Symmetry transformations include both connected and discrete groups.

Several exact solutions are derived using symmetry properties.

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.