Construction of scattering operators by the method of binary Darboux transformations
Abstract:
By using the binary Darboux transformations, we construct scattering
operators for a Dirac system with special potential depending on 2n
arbitrary functions of single variable. It is shown that one of the
operators coincides with the scattering operator obtained by Nyzhnyk in the
case of degenerate scattering data. It is also demonstrated that the
scattering operator for the Dirac system is either obtained as a
composition
of three Darboux self-transformations or factorized by two operators of
binary transformations of special form. We also consider several cases of
reduction of these operators.