Inverse scattering for waveguides in topological insulators
Mathematical Physics
2026-05-20 v2 Numerical Analysis
Analysis of PDEs
math.MP
Numerical Analysis
Abstract
This paper concerns the inverse scattering problem of a topologically non-trivial waveguide separating two-dimensional topological insulators. We consider the specific model of a Dirac system. We show that a short-range perturbation can be fully reconstructed from scattering data in a linearized setting and in a finite-dimensional setting under a smallness constraint. We also provide a stability result in appropriate topologies. We then solve the problem numerically by means of a standard adjoint method and illustrate our theoretical findings with several numerical simulations.
Cite
@article{arxiv.2512.22480,
title = {Inverse scattering for waveguides in topological insulators},
author = {Guillaume Bal and Xixian Wang and Zhongjian Wang},
journal= {arXiv preprint arXiv:2512.22480},
year = {2026}
}