Management of breather interactions

Abstract

We propose theoretically and confirm experimentally a general approach to manage multiple nonlinear interactions of coherent solitary wave structures on an unstable background---breathers. It allows adjusting the initial positions and phases of more than two moving breathers to observe various desired wave states at controllable moments of wave evolution. Our theoretical framework relies on exact multibreather solutions to the one-dimensional focusing nonlinear Schr\"odinger equation and asymptotic expressions describing shifts of breather positions and phases acquired by them in mutual collisions. As proof-of-principle, we consider a couple of separated pairs of breathers initially synchronized in a small-amplitude patterns; meanwhile, our approach can be generalized to other breather types and wave states. We obtain an explicit expression for the separation interval between the pairs so that the interactions of the breathers from the neighboring patterns lead to the formation of an extreme amplitude wave or recurrence to the initial small-amplitude state. Experiments are carried out on a light wave platform with a nearly conservative optical fiber system, which accurately reproduces the predicted dynamics and proves the viability of our nonlinear wave theory.