English

Solitons of the constrained Schr\"odinger equations

Exactly Solvable and Integrable Systems 2025-10-16 v2 Mathematical Physics math.MP

Abstract

We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton solutions for the discussed model. As an example of application of these results we present solitons of some vector nonlinear Schr\"odinger equation with gradient nonlinearity.

Keywords

Cite

@article{arxiv.2504.05816,
  title  = {Solitons of the constrained Schr\"odinger equations},
  author = {V. E. Vekslerchik},
  journal= {arXiv preprint arXiv:2504.05816},
  year   = {2025}
}