Zakharov-Shabat System With Constant Boundary Conditions. Reflectionless Potentials and end Point Singularities

Tihomir I. Valchev, Dublin Institute of Technology
Rossen Ivanov, Dublin Institute of Technology
Vladimir Stefanov Gerdjikov, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences

The present paper is published in “Integrability, Recursion Operators and Soliton Interactions”, Proc. of Int. Conference "Integrability, Recursion Operators and Soliton Interactions" on the occasion of Vladimir Gerdjikov’s 65th birthday, 29 - 31 August 2012, Sofia, Bulgaria, Eds.: B. Aneva, G. Grahovski, R. Ivanov and D. Mladenov, Avangard Prima, Sofia, Bulgaria, 2014, 301-324.


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.