Inverse scattering for the nonlinear magnetic Schrodinger equation

TL;DR

This paper investigates whether the scattering operator for a nonlinear magnetic Schrödinger equation can uniquely determine the magnetic potential, contributing to the understanding of inverse scattering problems in quantum mechanics.

Contribution

It establishes a uniqueness theorem showing that the magnetic potential can be uniquely recovered from the scattering data in the nonlinear Schrödinger setting.

Findings

Proves the uniqueness of magnetic potential reconstruction from scattering data

Extends inverse scattering theory to nonlinear magnetic Schrödinger equations

Provides mathematical foundation for potential recovery in quantum systems

Abstract

In this paper, we focus on the inverse scattering problem for the nonlinear Schrodinger equation with magnetic potentials. Specifically, we investigate whether the scattering operator associated with the nonlinear Schrodinger equation can uniquely determine the magnetic potential. Our main goal is to establish the uniqueness result for the magnetic potential based on the scattering data obtained from the scattering operator.