Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions

Abstract

AbstractIn this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix NLS systems on the line ($$-\infty<x<\infty$$ - ∞ < x < ∞ ) with certain physically relevant non-zero boundary conditions at space infinity, discuss some new developments and applications, and offer some perspectives about future directions on the subject.