Peregrine Rogue Wave dynamics in the continuous nonlinear Schr\"odinger system with parity-time symmetric Kerr nonlinearity

TL;DR

This paper investigates rogue wave dynamics in a parity-time symmetric nonlinear Schrödinger system, revealing the existence of Peregrine solitons and contrasting behaviors under unbroken and broken PT-symmetry regimes.

Contribution

It demonstrates the presence of Peregrine solitons in a PT-symmetric nonlinear Schrödinger system and explores their dynamics under different symmetry conditions.

Findings

Peregrine solitons exist in the PT-symmetric nonlinear Schrödinger system.

Low-intense Kuznetsov-Ma soliton trains appear without transverse shift.

High-intense Peregrine rogue waves occur with transverse shift in broken PT-symmetry.

Abstract

In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlinear Schrodinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrodinger system with PT-symmetric nonlinearity also admits Peregrine Soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine Rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.