Group analysis of the three-wave resonant system in (2+1) dimensions
- 1 November 1986
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (11), 2623-2628
- https://doi.org/10.1063/1.527280
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.Keywords
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