Inverse problem for the Schrödinger equation with non-self-adjoint matrix potential. (28th January 2021) - Avdonin, S A; Mikhaylov, A S; Mikhaylov, V S; Park, J C
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.