Peregrine rogue waves in the nonlocal nonlinear Schr\"odinger equation with parity-time symmetric self-induced potential

TL;DR

This paper investigates the interaction of Peregrine solitons in a nonlocal PT-symmetric nonlinear Schrödinger system, revealing complex wave dynamics including rogue waves and soliton trains through numerical simulations.

Contribution

It provides new insights into the nonlinear interactions and wave localization phenomena in nonlocal PT-symmetric NLSE systems using numerical analysis.

Findings

Kuznetsov-Ma soliton trains appear in the unbroken PT-phase when in phase.

Out of phase Peregrine solitons lead to repulsive nonlinear waves.

High-intensity rogue waves form within specific parameter ranges.

Abstract

In this work, based on the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlocal nonlinear Schr\"odinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects does the interaction of two first order Peregrine solitons have on the overall optical field dynamics. Upon numerical computation, we observe the appearance of Kuznetsov-Ma (KM) soliton trains in the unbroken PT-phase when the initial Peregrine solitons are in phase. In the out of phase condition, it shows repulsive nonlinear waves. Quite interestingly, our study shows that within a specific range of the interval factor in the transverse coordinate there exists a string of high intensity well-localized Peregrine rogue waves in the PT unbroken phase. We note that the interval factor as well as the transverse shift parameter play important roles in the nonlinear interaction and evolution dynamics of the optical fields. This could be important in developing fundamental understanding of nonlocal non-Hermitian NLSE systems and dynamic wave localization behaviors.