| Abstract: |
| We consider the dynamical system with boundary control for the vector Schr\"odinger 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 Dirichlet--to--Neumann operator. We begin by proving exact controllability of this system. We then provide a method to recover spectral data for the Schr\"odinger operator. Finally, we develop a strategy to solve the inverse problem using techniques of the Boundary Control method. |
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