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.

中文翻译：

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非局部逆空间非线性Schrödinger层次结构的逆散射变换和孤子解

本文的目的是通过特征值问题的非局部群约简来构建非局部逆空间非线性薛定ding（NLS）层次结构，并生成其逆散射变换和孤子解。逆散射问题由确定广义矩阵Jost本征函数的Riemann-Hilbert问题公式化。Sokhotski-Plemelj公式用于将Riemann-Hilbert问题转换为Gelfand-Levitan-Marchenko型积分方程。提出了对应于无反射变换的，带有身份跳变矩阵的特殊Riemann-Hilbert问题的解公式，并将其应用于非局部NLS层次的孤子解。