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We consider scalar defocusing nonlinear Schroedinger equation with constant boundary conditions. We aim here to provide a self contained pedagogical exposition of the most important facts regarding integrability of that classical evolution equation. It comprises the following topics: direct and inverse scattering problem and the dressing method.
Valchev, T., Ivanov, R. & Gerdjikov, V. (2014). Zakharov-Shabat system with constant boundary conditions. Reflectionless potentials and end point singularities. Integrability, Recursion Operators and Soliton Interactions,, Avangard Prima, Sofia. pg. 301-324. doi:10.21427/xtej-a952