Recovery of a spatially-dependent coefficient from the NLS scattering map

TL;DR

This paper investigates the inverse scattering problem for nonlinear Schrödinger equations with spatially-dependent nonlinearities, aiming to recover the coefficient function from scattering data.

Contribution

It extends previous work by analyzing the recovery of spatially-dependent coefficients in nonlinear Schrödinger equations from scattering maps.

Findings

Established conditions for unique recovery of the coefficient.

Developed a method to reconstruct the coefficient from scattering data.

Demonstrated the approach with theoretical results.

Abstract

We follow up on work of Strauss, Weder, and Watanabe concerning scattering and inverse scattering for nonlinear Schr\"odinger equations with nonlinearities of the form $\alpha(x)|u|^p u$.