Geodesic
Characteristic properties of scattering data for discontinuous Schr\"{o}dinger equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 95-102.

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In this paper, we discuss the inverse scattering problem to recover the potential from the scattering data of a class of Schrödinger equations with a nonlinear spectral parameter in the boundary condition. It turns out that for real-valued potential function $q(x)$, the scattering data is defined as in the non-self-adjoint case: the scattering function, the nonreal singular values, and normalization polynomials. Characteristic properties of the spectral data are investigated. The solution of the problem is constructed by using the Gelfand–Levitan–Marchenko procedure. The uniqueness of the algorithm for the potential with given scattering data is proved.
Keywords: scattering data, normalization polynomial, scattering problem on a half-line, nonlinear spectral parameter. 
@article{INTO_2017_141_a7,
     author = {Kh. R. Mamedov},
     title = {Characteristic properties of scattering data for discontinuous {Schr\"{o}dinger} equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {95--102},
     publisher = {mathdoc},
     volume = {141},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_141_a7/}
}
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Kh. R. Mamedov. Characteristic properties of scattering data for discontinuous Schr\"{o}dinger equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 95-102. http://geodesic.mathdoc.fr/item/INTO_2017_141_a7/