Solitons, breathers and rogue waves in a reverse time nonlocal generalized nonlinear Schrödinger equation with four-wave mixing effect

Under investigation is a reverse time nonlocal generalized nonlinear Schr & ouml;dinger equation, which can be derived from a special reduction of the coupled generalized nonlinear Schr & ouml;dinger equations with four-wave mixing effect. The N-fold Darboux transformation related to a 3x3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 3$$\end{document} matrix spectral problem with two symmetry relationships has been constructed. As an application, the N-soliton solution under zero background as well as the N-breather and Nth-order rogue wave solutions under nonzero background have been obtained. The dynamic behaviors of bright one- and two-solitons are demonstrated. The Kuznetsov-Ma breather, Akhmediev breather, the fission, fusion and crossing of breathers, and the hybrid types of breathers are presented. Furthermore, first- and second-order rogue waves and the interactions between rogue waves and breathers are discussed through graphical simulations.