Inverse spectral problem for Dirac operator with discontinuous coefficient and polynomials in boundary condition

In this work, the inverse scattering problem for Dirac equations system with discontinuous coefficient and higher order polynomials of spectral parameter in the boundary condition is considered. The scattering function of the problem is defined, and its properties are investigated. The Marchenko-type main equation is obtained and it is shown that the potential is uniquely recovered by the scattering function. A generalization of Marchenko method is given for a class of Dirac operator.