A class of potentials for the nonstationary Dirac equation

A class of nonstationary potentials for the massive Dirac equation in two-dimensional space -time is constructed and studied by the inverse scattering problem method. The $S$-matrix of these potentials is diagonal in the energy representation. The completeness of the wave operators is proved under certain assumptions on the potential. A reflection-free potential connected with the double soliton in the Gross–Neveu model is analyzed as an example.