Stability estimates for the recovery of the nonlinearity from scattering data

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

(i \partial_{t} + Δ) u = a (x) | u |^{p} u

in three space dimensions, with $p \in [\frac{4}{3}, 4]$ and $a \in W^{1, \infty}$ .

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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

Vol. 6, No. 1, 2024

Gong Chen and Jason Murphy

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors