Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schr\"odinger models

TL;DR

This paper introduces novel multi-parametric vector rogue wave solutions with parity-time symmetry in n-component nonlinear Schrödinger systems, revealing their properties, conditions for high amplitudes, and effects of model deformations, aiding experimental design.

Contribution

It presents the first explicit multi-parametric PT-symmetric vector rogue wave solutions in n-component NLS models, including conditions for high amplitudes and effects of non-integrable deformations.

Findings

Explicit PT-symmetric vector rogue wave solutions are constructed.

Parameter constraints can induce high-amplitude rogue waves.

Non-integrable deformations influence rogue wave excitation.

Abstract

The extreme events are investigated for an $n$-component nonlinear Schr\"odinger ($n$-NLS) system in the focusing Kerr-like nonlinear media, which appears in many physical fields. We report and discuss the novel multi-parametric families of vector rational rogue wave (RW) solutions featuring the parity-time (PT) symmetry, which are characterized by non-identical boundary conditions for the components, and consistent with the degeneracy of $n$ branches of Benjamin-Feir instability. Explicit examples of PT-symmetric vector RWs are presented. Some parameter constraints can make some components generate the RWs with high amplitudes due to many-body resonant interactions.Effect of a non-integrable deformation of the model on the excitation of vector RWs is also discussed. These results will be useful to design the RW experiments in multi-component physical systems.