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}
}