Vector breathers in the Manakov system
Andrey Gelash, Anton Raskovalov

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…
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Taxonomy
TopicsNonlinear Photonic Systems · Nonlinear Waves and Solitons · Advanced Mathematical Physics Problems
