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.
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