On the nonlinear Schr\"odinger equation with a time-dependent boundary condition
Exactly Solvable and Integrable Systems
2020-08-11 v1
Abstract
We study the nonlinear Schr\"odinger equation on the half-line with a boundary condition that involves time derivative. This boundary condition was presented by Zambon [J. High Energ. Phys. 2014 (2014) 36]. We establish the integrability of such a boundary both by using the Sklyanin's formalism and by using the tool of B\"acklund transformations together with a suitable reduction of reflection type. Moreover, we present a method to derive explicit formulae for multi-soliton solutions of the boundary problem by virtue of the Darboux transformation method in conjunction with a boundary dressing technique.
Cite
@article{arxiv.2008.03955,
title = {On the nonlinear Schr\"odinger equation with a time-dependent boundary condition},
author = {Baoqiang Xia},
journal= {arXiv preprint arXiv:2008.03955},
year = {2020}
}