Space-phase shifts acquiring by breathers after mutual collisions

The key result of this work is the first theoretical computation of exact expressions describing space and phase shifts acquiring by breathes after mutual collisions in the framework of the focusing one-dimensional nonlinear Schrödinger equation (NLSE) model [1]. Similar expressions are the backbone of soliton theory, where they allow to predicts soliton interaction dynamics and introduce statistical description of soliton gas in terms of kinetic equation. Theory of breathers – solitary type wave groups on an unstable background – has been developing almost as long as theory of solitons. However, up to now, this important part of theory has been missing.

In our work we present space and phase shift formulas for the NLSE breathers and demonstrate how they can be used to go deeply in understanding of an intriguing nonlinear phenomena – formation rogue waves from a calm background. With these formulas we show that synchronized collisions of breathers are the central mechanism of extreme amplitude wave formation as a result of modulation instability development. We illustrate this conclusion by particular examples of multi-breather dynamics as well as by statistical analysis of multi-breather interactions. In comparison to the work [1], here we also analyse the impact of the effects lying beyond the NLSE model on the multi-breather synchronization. Finally, we present new scenarios of the synchronised multi-breather interactions, that can be observed in laboratory experiments.

The work was supported by the RFBR grant No. 19-31-60028.

[1] A. A. Gelash, Formation of rogue waves from a locally perturbed condensate, Phys. Rev. E 97, 022208 (2018).