On Certain Symmetry Reduction Systems of the Three-Wave Resonant Interaction in (2+1) Dimensions
- 1 October 1986
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 76 (4) , 739-751
- https://doi.org/10.1143/ptp.76.739
Abstract
We study three systems of nonlinear differential equations obtained from the symmetry reduction of the three-wave resonant interaction (2D-3WR) in (2+1) dimensions. We show that two of such systems are reducible to Painlevé III and Painlevé VI equations, respectively, while for the third system a spectral problem is found via a prolongation tecnique. New solutions of the 2D-3WR equations can be determined through the relationships existing between the reduction variables and the original three-wave resonant fields.Keywords
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