• Corpus ID: 221090115

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

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



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