Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations - MA, WEN-XIU; HUANG, YEHUI; WANG, FUDONG (European journal of applied mathematics, 2022)
The aim of the paper is to explore non-local reverse-space matrix non-linear Schrödinger equations and their inverse scattering transforms. Riemann–Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski–Plemelj formula is used to determine Gelfand–Levitan–Marchenko-type integral equations for generalised matrix Jost solutions. Soliton solutions are constructed through the reflectionless transforms associated with poles of the Riemann–Hilbert problems.