A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation

Abstract

In this paper, a novel Riemann–Hilbert (RH) approach is reported for a physically significant nonlocal integrable nonlinear Schrödinger equation. In this RH approach, the spectral analysis is performed from the t-part of the Lax pair rather than the x-part to formulate the desired RH problem. As a consequence, the resulting RH problem is determined by the t-part of the Lax pair with the x-part playing an auxiliary role. Compared with the traditional RH method, the novel RH approach in this paper has the merits that (a) the symmetry relations of the scattering data are found to be simple, (b) the general multi-soliton solutions of the equation can be easily obtained in the reflectionless cases. Additionally, to show the remarkable features of the obtained multi-soliton solutions, some special soliton dynamics are theoretically explored and then graphically illustrated by demonstrating their three-dimensional profiles.