Geodesic
Direct and inverse scattering problems for the perturbed Hill difference equation
Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1529-1552

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The direct and inverse scattering problems are studied for the perturbed Hill equation $(\widehat a_{n-1}+a_{n-1})y_{n-1} +(\,\widehat b_n+b_n)y_n+(\widehat a_n+a_n)y_{n+1}=\lambda y_n$, $n\in\Bbb Z$. The perturbation coefficients $a_n$, $b_n$ are reconstructed from the periodic coefficients $\widehat a_n$, $\widehat b_n$ and the scattering data. 
@article{SM_2005_196_10_a5,
     author = {Ag. Kh. Khanmamedov},
     title = {Direct and inverse scattering problems for the perturbed {Hill} difference equation},
     journal = {Sbornik. Mathematics},
     pages = {1529--1552},
     publisher = {mathdoc},
     volume = {196},
     number = {10},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_10_a5/}
}
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Ag. Kh. Khanmamedov. Direct and inverse scattering problems for the perturbed Hill difference equation. Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1529-1552. http://geodesic.mathdoc.fr/item/SM_2005_196_10_a5/