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Stability estimates for the recovery of the nonlinearity from scattering data

Gong Chen and Jason Murphy

Vol. 6 (2024), No. 1, 305–317
DOI: 10.2140/paa.2024.6.305
Abstract

We prove stability estimates for the problem of recovering the nonlinearity from scattering data. We focus our attention on nonlinear Schrödinger equations of the form

(it + Δ)u = a(x)|u|pu

in three space dimensions, with p [4 3,4] and a W1,.

Keywords
NLS, scattering, inverse scattering, stability
Mathematical Subject Classification
Primary: 35Q55
Milestones
Received: 10 May 2023
Revised: 23 July 2023
Accepted: 30 October 2023
Published: 22 February 2024
Authors
Gong Chen
Georgia Institute of Technology
Atlanta, GA
United States
Jason Murphy
Missouri University of Science & Technology
Rolla, MO
United States