Increasing stability of a linearized inverse boundary value problem for a nonlinear Schr\"odinger equation on transversally anisotropic manifolds
Analysis of PDEs
2023-01-20 v1
Abstract
We consider the problem of recovering a nonlinear potential function in a nonlinear Schr\"odinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex geometric optics (CGO) solutions according to the wavenumber, we prove the increasing stability of recovering the coefficient of a cubic term as the wavenumber becomes large.
Keywords
Cite
@article{arxiv.2301.07875,
title = {Increasing stability of a linearized inverse boundary value problem for a nonlinear Schr\"odinger equation on transversally anisotropic manifolds},
author = {Shuai Lu and Jian Zhai},
journal= {arXiv preprint arXiv:2301.07875},
year = {2023}
}