Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds

Xi Chen; Shuai Lu; Ruochong Zhang

Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds

Analysis of PDEs 2026-07-20 v1

Authors: Xi Chen , Shuai Lu , Ruochong Zhang

Abstract

We study the recovery of a smooth nonlinearity in semilinear wave equations on globally hyperbolic Lorentzian manifolds. Our approach combines higher-order linearization with distorted plane waves and Gaussian beams, using three-wave, four-wave, and m-wave interactions to recover different Taylor coefficients.

Keywords

inverse problems semilinear wave equations Lorentzian manifolds higher-order linearization Gaussian beams

Cite

@article{arxiv.2607.17501,
  title  = {Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds},
  author = {Xi Chen and Shuai Lu and Ruochong Zhang},
  journal= {arXiv preprint arXiv:2607.17501},
  year   = {2026}
}