Group analysis of the three-wave resonant system in (2+1) dimensions

Abstract

The three-wave resonant interaction equations (2D-3WR) in two spatial and one temporal dimension within a group framework are analyzed. The symmetry algebra of this system, which turns out to be an infinite-dimensional Lie algebra whose subalgebra is of the Kac–Moody type, is found. The one- and two-dimensional symmetry subalgebras are classified and the corresponding reduction equations are obtained. From these the new invariant and the partially invariant solutions of the original 2D-3WR equations are obtained.