Vector breathers in the Manakov system

TL;DR

This paper analyzes vector breather interactions in the Manakov system, revealing different dispersion branches, collision dynamics, and their role in modulation instability development.

Contribution

It provides a theoretical framework for multi-breather solutions, classifies breather types, and derives formulas for their interactions and asymptotic behaviors.

Findings

Type I breathers participate in modulation instability.

Collision formulas describe phase and space shifts.

Resonance phenomena relate to eigenvalue merging.

Abstract

We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dimensional focusing nonlinear Schrodinger equation -- the Manakov system. With the dressing method, we generate the multi-breather solutions to the Manakov model. As shown previously in [D. Kraus, G. Biondini, and G. Kovacic, Nonlinearity 28, 310, 2015] the class of vector breathers is presented by three fundamental types I, II, and III. Their interactions produce a broad family of the two-component (polarized) nonlinear wave patterns. First, we demonstrate that the type I and the types II and III correspond to two different branches of the dispersion law of the Manakov system in the presence of the unstable background. Then we investigate the key interaction scenarios, including collisions of standing and moving breathers and resonance breather transformations. Analysis of the two-breather solution allows us to derive general formulas describing phase and space shifts acquired by breathers in mutual collisions. The found expressions enable us to describe the asymptotic states of the breather interactions and interpret the resonance fusion and decay of breathers as a limiting case of infinite space shift in the case of merging breather eigenvalues. Finally, we demonstrate that only type $\mathrm{I}$ breathers participate in the development of modulation instability from small-amplitude perturbations within the superregular scenario, while the breathers of types $\mathrm{II}$ and $\mathrm{III}$, belonging to the stable branch of the dispersion law, are not involved in this process.