Competing mechanisms of nonlinear modulation instability

Stefano Trillo
Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy
The nonlinear stage of modulation instability (MI) is extremely rich. For periodic perturbations multiple recurrences occurs according to a complex homoclinic structure that represents the continuation of MI in the depleted stage. When the perturbation becomes localized the MI recurrences break down and different scenarios are possible. A quite universal scenario is the development of an auto-modulation, i.e. a strongly oscillating structure within a characteristic wedge-shaped region that smoothly connect to the background. However, for sufficiently generic perturbations the auto-modulation can be accompanied by the emission of breather pairs. In this talk we discuss how to predict the parameters of such breathers in terms of simple formulas.