Lax and Levermore showed that solutions of the Korteweg-de Vries equation in the small-dispersion limit exhibit rapid oscillations within slowly modulated envelopes. Similar behavior was shown for the focusing integrable nonlinear Schrödinger equation by Kamvissis, McLaughlin, and Miller using so-called semiclassical soliton ensembles, which are pure soliton intial data intended to approximate more general initial data in the zero-dispersion limit. After providing a brief overview of applications of semiclassical soliton ensembles to dispersive equations such as the sine-Gordon and modified nonlinear Schrödinger equations, we will discuss some recent results (joint with Robert Jenkins and Peter Miller) for the three-wave resonant interaction equations. Despite the fact that these equations are non-dispersive, the semiclassical soliton ensembles exhibit the same qualitative behavior.