5 papers
Numerical reconstruction of polygonal obstacles by diffracted waves
Xi Chen, Kuangmiao Xiong, Boxi Xu
We present a numerical method for recovering rigid polygonal obstacles in two dimensions, based on the diffraction-based inverse scattering theory of Bao, Chen, Lu, and Xiong. A si…
Inverse Geometric Diffraction by a Cone
Gang Bao, Xi Chen, Shuai Lu +1
Consider the inverse problem of recovering a strictly convex conical obstacle in from the diffraction coefficients along with arrival directions (lens data) or arriv…
Inverse Scattering by Diffracted Waves
Gang Bao, Xi Chen, Shuai Lu +1
In addition to reflection and refraction, another form of wave deviation is defined as diffraction. Notably, when incident waves strike a corner, diffracted waves emanate from the…
Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds
Xi Chen, Shuai Lu, Ruochong Zhang
We study the recovery of a smooth nonlinearity in semilinear wave equations on globally hyperbolic Lorentzian manifolds. Our approach combines higher-order linearization with disto…
Stable inversion of potential in nonlinear wave equations with cubic nonlinearity
Xi Chen, Shuai Lu, Ruochong Zhang
This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower o…