Riemann–Hilbert approach and soliton analysis of a novel nonlocal reverse-time nonlinear Schrödinger equation

By imposing a nonlocal reverse-time type constraint on a general coupled nonlinear Schrödinger (NLS) equation, we propose a novel nonlocal reverse-time NLS equation which involves a free real parameter and a free complex parameter. The introduced nonlocal NLS equation is integrable since it admits a 3×3\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 Lax pair formulation. By solving the proposed nonlocal NLS equation, one can obtain the soliton solutions of the general coupled NLS equation with special initial conditions. By extending the Riemann–Hilbert (RH) approach to the proposed nonlocal NLS equation, we further explore and reveal its spectral structure in detail which is different from that of the general coupled NLS equation, from which three types of soliton solutions are rigorously obtained. In addition, the soliton analysis is performed to reveal the soliton dynamical behaviors underlying the soliton solutions.