Advanced Mathematical Models & Applications

The work is devoted to the study of an inverse problem for the Dirac operator with a real coefficient. One of the boundary conditions is separated, while the other is non-separated. The non-separated boundary condition contains a linear function of the spectral parameter. The asymptotics of the spectrum of the Dirac operator are derived, a uniqueness theorem is proved, and an algorithm for solving the inverse problem of reconstructing boundary value problems from spectral data is constructed, where the spectral data consist of the spectra of two problems. From these spectral data, the characteristic functions of the boundary value problems are first reconstructed in the form of infinite products, along with the parameters of the boundary conditions. The problem is then reduced to the inverse problem of reconstructing the coefficient of the Dirac equation from the spectra of two boundary value problems with separated boundary conditions. The results of the paper can be used to solve various variants of inverse problems in the spectral analysis of differential operators, as well as to integrate certain nonlinear equations of mathematical physics.