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The three-wave resonant interaction equations are a non-dispersive system ofpartial differential equations with quadratic coupling describing the timeevolution of the complex amplitudes of three resonant wave modes. Collisions ofwave packets induce energy transfer between different modes via pumping anddecay. We analyze the collision of two or three packets in the semiclassicallimit by applying the inverse-scattering transform. Using WKB analysis, weconstruct an associated semiclassical soliton ensemble, a family ofreflectionless solutions defined through their scattering data, intended toaccurately approximate the initial data in the semiclassical limit. The mapfrom the initial packets to the soliton ensemble is explicit and amenable toasymptotic and numerical analysis. Plots of the soliton ensembles indicate thespace-time plane is partitioned into regions containing either quiescent,slowly varying, or rapidly oscillatory waves. This behavior resembles thewell-known generation of dispersive shock waves in equations such as theKorteweg-de Vries and nonlinear Schrodinger equations, although the physicalmechanism must be different in the absence of dispersion.

Semiclassical soliton ensembles for the three-wave resonant interaction equations