Recovery of the matrix potential of the one-dimensional Dirac equation from spectral data

A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand-Levitan equation and the Fourier-Legendre series expansion of the transmutation kernel. A linear algebraic system of equations is obtained, which can be solved numerically. To the best of our knowledge, this is the first practical method for the solution of the inverse problem for the one-dimensional Dirac equation on a finite interval.