Integrable models in nonlinear optics and soliton solutions

Nonlinear optics, more than other subjects, has surprisingly produced quite a number of approximate models which are integrable. Here we briefly mention these models with the aim of showing contacts between the mathematical and applicative sides of the theory of integrable dynamical systems. In particular, we illustrate the recent impact of boomeronic-type wave equations on applicative issues in the special context of the resonant interaction of three waves.