Characteristics of rogue waves in the scalar and vector nonlocal nonlinear Schrödinger equations

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.