Two simultaneous nonlocal group constraints of the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems are discussed, of which one constraint changes the eigenvalue parameter into its negative of the complex conjugate and the other constraint does not change the eigenvalue parameter. Under those two constraints, mixed-type nonlocal integrable nonlinear Schrödinger hierarchies are generated. Further, based on specific distributions of eigenvalues and adjoint eigenvalues, a formulation of soliton solutions is established via the corresponding reflection-less generalized Riemann-Hilbert problems, where eigenvalues and adjoint eigenvalues could be equal.

中文翻译：

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(-λ*,λ) 类型的可积非局部非线性薛定谔层次结构和孤子解

讨论了Ablowitz-Kaup-Newell-Segur矩阵特征值问题的两个同时非局部群约束，其中一个约束将特征值参数改变为复共轭的负值，另一个约束不改变特征值参数。在这两个约束下，生成混合型非局部可积非线性薛定谔层次结构。进一步，基于特征值和伴随特征值的特定分布，通过相应的无反射广义黎曼-希尔伯特问题建立孤子解的公式，其中特征值和伴随特征值可以相等。