A novel general nonlocal reverse-time nonlinear Schrödinger equation and its soliton solutions by Riemann–Hilbert method

In this paper, a novel general nonlocal reverse-time nonlinear Schrödinger (NLS) equation involving two real parameters is proposed from a general coupled NLS system by imposing a nonlocal reverse-time constraint. In this sense, the proposed nonlocal equation can govern the nonlinear wave propagations in such physical situations where the two components of the general coupled NLS system are related by the nonlocal reverse-time constraint. Moreover, the proposed nonlocal equation can reduce to a physically significant nonlocal reverse-time NLS equation in the literature. Based on the Riemann–Hilbert (RH) method, we also explore the complicated symmetry relations of the scattering data underlying the proposed nonlocal equation induced by the nonlocal reverse-time constraint, from which three types of soliton solutions are successfully obtained. Furthermore, some specific soliton dynamical behaviors underlying the obtained solutions are theoretically explored and graphically illustrated.