# 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} }

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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