Rational reflection coefficients in inverse scattering for a Dirac system

The inverse scattering problem (ISP) on the whole line for a Dine system is considered. The reflection coefficient (FC) is represented as a rational f unction with an arbitrary number of poles. The method of solving for the Ge l' fand-Levitan-Marchenko (GLM) equation generated by a rational reflection coefficient (RFC) is extended to n poles, when a spectral gap is present. The explicit solution in the case of three poles is presented. Graphs of th e potential as a function of distance are displayed for cases having up to four poles.