On an inverse scattering problem with a discontinuous coefficient On the whole line

Abstract

This paper is devoted to study the inverse scattering problem of a generalized Sturm-Liouville equation on the whole line.The solutions of the considered problem and their asymptotic behaviour are presented.The expansion by eigenfunctions of the considered problem and hence Parseval equations are given.The right and left scattering data are obtained. The inverse scattering problem is formulated and completely solved.