• Corpus ID: 221090115

On the nonlinear Schr\"odinger equation with a time-dependent boundary condition.

@article{Xia2020OnTN,
  title={On the nonlinear Schr\"odinger equation with a time-dependent boundary condition.},
  author={Baoqiang Xia},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2020}
}

• B. Xia
• Published 10 August 2020
• Mathematics
• arXiv: Exactly Solvable and Integrable Systems

We study the nonlinear Schrodinger 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 Backlund 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.