# Solutions of the nonlocal nonlinear Schr\"odinger hierarchy via reduction

## TL;DR

This paper introduces a method to derive solutions for the nonlocal nonlinear Schrödinger hierarchy from known solutions of the AKNS hierarchy using reduction techniques, presenting some new solutions in double Wronskian form.

## Contribution

It provides a general approach to obtain nonlocal solutions from local ones for integrable systems with double Wronskian solutions, applicable beyond the Schrödinger hierarchy.

## Key findings

- Derived new nonlocal solutions in double Wronskian form.
- Established a reduction-based method for nonlocal integrable systems.
- Demonstrated the approach's applicability to other systems.

## Abstract

In this letter we propose an approach to obtain solutions for the nonlocal nonlinear Schr\"{o}dinger hierarchy from the known ones of the Ablowitz-Kaup-Newell-Segur hierarchy by reduction. These solutions are presented in terms of double Wronskian and some of them are new.The approach is general and can be used for other systems with double Wronskian solutions which admit local and nonlocal reductions.