Inverse scattering transforms and soliton solutions of nonlocal reverse-space nonlinear Schrodinger hierarchies

The aim of the paper is to construct nonlocal reverse-space nonlinear Schrodinger (NLS) hierarchies through nonlocal group reductions of eigenvalue problems and generate their inverse scattering transforms and soliton solutions. The inverse scattering problems are formulated by Riemann-Hilbert problems which determine generalized matrix Jost eigenfunctions. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A solution formulation to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless transforms, is presented and applied toN-soliton solutions of the nonlocal NLS hierarchies.