A. G. Ramm
Published 2016-01-08Version 1
The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inversion procedure is discussed and a new set of necessary and sufficient conditions on the scattering data is given for the scattering data to be generated by a potential suitable potential. Our proof is new and in contrast with known proof it does not use equations on the negative half-line.
Journal: Reports on Math. Phys (ROMP), 76, N2, (2015), 159-169
Inverse scattering problem for a special class of canonical systems and non-linear Fourier integral. Part I: asymptotics of eigenfunctions
Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave
The generalized Marchenko method in the inverse scattering problem for a first-order linear system
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