Direct Problem of Scattering Theory for a Dirac System of Differential Equations on the Half-Line in the Case of Finite Density

In this paper, we study the direct scattering problem on the half-line for the Dirac systemof differential equations in the case of finite density with the boundary condition \(y_{1}(0)=y_{2}(0)\) . The spectrum is studied, the resolvent isconstructed, and the spectral expansion in the eigenfunctions of the Dirac operator is obtained.