English

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}
}