Numerical simulation of breather dynamics

The numerical simulation of the so-called breather turbulence (dynamics of breather ensembles) is performed within the integrable model of modified Korteweg – de Vries equation. Two-breather interaction is considered as an elementary act of the breather turbulence. The possible modes of breather-breather or breather-soliton interactions have been investigated. The influence of such interactions on multi-breather dynamics and its statistical characteristics has been analyzed. The results of direct numerical simulation of breather focusing with “non-optimal” phases allow finding the probability of a possible collision of more than two breathers. The formation of abnormally large pulses (rogue waves) in random ensembles of breathers has been demonstrated.