Ufa Mathematical Journal
    Volume 8, Number 4, pp. 42-51

    Darboux transformations in the inverse scattering problem

    Badakhov M.Sh., Shabat A.B.


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    As it is know, Darboux transformations play a key role in applications in ISP. In the paper we expose the theory of such transformations for the Schrödinger equations with compactly supported potential, which are not necessarily smooth. We study a new class of transformations connected with the zeroes of the reflection coefficient located at conjugated points in the complex plane.