The inverse scattering problem for a reflectional system

The general solution to the inverse scattering problem for a reflectional system is formulated. Two families of eigenfunctions, corresponding to the continuous and discrete spectra, are introduced to transform the Gel'fand-Levitan integral equation to a system of N+1 equations. Making use of the available soliton solution, it is shown that the inverse scattering problem can be reduced to one of solving the eigenfunction for a continuous spectrum only. In addition, the properties of these eigenfunctions are also investigated.