A1 Journal article (refereed)
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities (2022)

Lu, S., Salo, M., & Xu, B. (2022). Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities. Inverse Problems, 38(6), Article 065009. https://doi.org/10.1088/1361-6420/ac637a

JYU authors or editors

Publication details

All authors or editors: Lu, Shuai; Salo, Mikko; Xu, Boxi

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2022

Publication date: 02/04/2022

Volume: 38

Issue number: 6

Article number: 065009

Publisher: IOP Publishing

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/ac637a

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/80493

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2111.13446

Abstract

We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schrödinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearity in solving the inverse Schrödinger potential problem. Noticing that both linearization approaches can be numerically approximated, we provide several reconstruction algorithms for the quadratic and general power type nonlinearity terms, where one of these algorithms is designed based on boundary measurements of multiple wavenumbers. Several numerical examples shed light on the efficiency of our proposed algorithms.

Keywords: inverse problems; partial differential equations

Free keywords: increasing stability; inverse Schrödinger potential problem; power type nonlinearities; reconstruction algorithms

Contributing organizations

Related projects

Ministry reporting: Yes

Reporting Year: 2022

Preliminary JUFO rating: 2