Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies

Abstract

Abstract The aim of the paper is to construct nonlocal reverse‐space nonlinear Schrödinger (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 to ‐soliton solutions of the nonlocal NLS hierarchies.