Loop Algebra Splitting and Darboux Transformations for Nonlocal Derivative Nonlinear Schrödinger Hierarchies

Ziqi Li; Zhiwei Wu

Loop Algebra Splitting and Darboux Transformations for Nonlocal Derivative Nonlinear Schrödinger Hierarchies

Exactly Solvable and Integrable Systems 2026-07-26 v1

Authors: Ziqi Li , Zhiwei Wu

Abstract

We develop a unified algebraic framework for nonlocal derivative nonlinear Schr\"odinger (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.

Keywords

loop algebra splitting nonlocal dnls darboux transformations integrable hierarchies reverse space-time reductions explicit solutions

Cite

@article{arxiv.2607.23422,
  title  = {Loop Algebra Splitting and Darboux Transformations for Nonlocal Derivative Nonlinear Schrödinger Hierarchies},
  author = {Ziqi Li and Zhiwei Wu},
  journal= {arXiv preprint arXiv:2607.23422},
  year   = {2026}
}

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