Inverse problem for the Schrödinger equation with non-self-adjoint matrix potential. (28th January 2021)

• Record Type: Journal Article
• Authors: Avdonin, S A; Mikhaylov, A S; Mikhaylov, V S; Park, J C
• Is Part Of: Inverse problems. Volume 37:Number 3(2021)
• Publication Date: 2021-01-28
• Subjects: inverse problem -- Schrödinger equation -- matrix potential -- controllability -- boundary control method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abd7cb
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the dynamical system with boundary control for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the dynamical Neumann-to-Dirichlet operator. We first provide a method to recover spectral data for the Schrödinger system and consequently prove controllability of the system. We then develop a strategy for solving the inverse problem using this method with other techniques of the boundary control method.