AI 中文总结
该研究为非局部导数非线性薛定谔型层级开发统一代数框架，基于环代数分裂，通过代数约束实现约化，推导达布变换并用于构造显式解。
AI 中文摘要
我们基于环代数分裂为非局部导数非线性薛定谔（DNLS）型层级开发了一个统一的代数框架。在此框架内，通过代数约束实现非局部和逆时空约化，得到相应的可积层级。通过构造简单元素并建立相关因式分解理论，我们推导了达布变换（DTs）并应用其构造显式解。
英文摘要
We develop a unified algebraic framework for nonlocal derivative nonlinear Schrödinger (DNLS)-type hierarchies based on loop algebra splittings. Within this framework, nonlocal and reverse space-time reductions are realized through algebraic constraints, leading to the corresponding integrable hierarchies. By constructing simple elements and establishing the associated factorization theory, we derive Darboux transformations (DTs). And apply DTs to construct explicit solutions.
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