A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation

• Published in: Communications on pure and applied mathematics Vol. 72; no. 8; pp. 1722 - 1805
• Main Authors: Bilman, Deniz, Miller, Peter D.
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.08.2019
• Subjects: Asymptotic methods; Asymptotic properties; Boundary conditions; Dynamic stability; Inverse scattering; Schrodinger equation; Singularity (mathematics); Structural stability; Transformations (mathematics)

We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other equations by natural generalization) formulated with nonzero boundary conditions at infinity. The purpose is to deal with arbitrary‐order poles and potentially severe sp...