Characteristics of rogue waves in the scalar and vector nonlocal nonlinear Schr\"{o}dinger equations

TL;DR

This paper derives higher-order rogue wave solutions for nonlocal nonlinear Schrödinger equations with parity-time symmetry, revealing complex dynamics and patterns not seen in local equations, using Darboux transformation techniques.

Contribution

It introduces a method to obtain higher-order rogue wave solutions for nonlocal NLSEs and explores their unique characteristics and dynamics.

Findings

Rich, complex rogue wave patterns identified

Most solutions have no counterparts in local equations

Solutions obtained via Darboux transformation

Abstract

In this paper, general higher-order rogue wave solutions of the parity-time ($\mathcal {P}\mathcal {T}$) symmetric scalar and coupled nonlocal nonlinear Schr\"{o}dinger equations (NLSEs) are calculated theoretically via a Darboux transformation by a separation of variable technique. Furthermore, in order to understand these solutions better, the main characteristics of the obtained solutions are explored clearly and conveniently. Our results show that the dynamics of these solutions exhibits rich patterns, most of which have no counterparts in the corresponding local equations.