Inverse scattering on the line for a generalized nonlinear Schroedinger equation
Tuncay Aktosun, Vassilis G. Papanicolaou, Vassilis Zisis
TL;DR
This paper studies the inverse scattering problem for a one-dimensional generalized nonlinear Schrödinger equation with compactly supported, wave-function-dependent potentials, establishing conditions for unique potential recovery from scattering data.
Contribution
It introduces a framework for solving the inverse scattering problem for a generalized nonlinear Schrödinger equation with wave-function-dependent potentials, proving uniqueness of potential recovery.
Findings
Unique potential recovery from scattering data
Analysis of inverse scattering for nonlinear Schrödinger equations
Potential depends on the wave function
Abstract
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the potential is established from an appropriate set of scattering data.
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