Geodesic
On the inverse scattering problem for a class of Sturm--Liouville operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 81-86

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On the positive semi-infinite interval, we consider the inverse scattering problem for the Sturm–Liouville operator with a quadratic polynomial of the spectral parameter in the boundary condition. We define the scattering data of the problem and examine its properties. We derive the main integral equation and show that the potential is uniquely recovered.
Keywords: inverse problem, scattering function, scattering data, spectral parameter, Sturm–Liouville operator. 
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     author = {Kh. R. Mamedov and U. Demirbilek},
     title = {On the inverse scattering problem for a class of {Sturm--Liouville} operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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Kh. R. Mamedov; U. Demirbilek. On the inverse scattering problem for a class of Sturm--Liouville operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 81-86. http://geodesic.mathdoc.fr/item/INTO_2021_200_a8/