Abstract
Inverse scattering for the Schrodinger equation on the line is studied for reflection and transmission coefficients that satisfy the usual regularity conditions and are rational functions ofk. The origin is still a particular point, but the potentials do not need to be cut at this point like in previous studies. Giving up this restriction corresponds to the existence of poles for both reflection coefficients in both upper and lower halfk-planes. It is shown that the problem reduces to solving a linear algebraic system. A different algorithm, made of a sequence of Darboux-Backlund transforms, gives also the solution in closed form and enables to study separately modifications of both sides of the potential due to the introduction of poles. Thus it paves the way for approximation studies. Generalizations and particular problems will be studied in forthcoming papers.
Published Version
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