Geodesic
An inverse scattering problem for a~perturbed Hill's operator
Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 831-843.

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We consider the inverse scattering problem for the operator $L=-d^2/dx^2+p(x)+q(x)$, $x\in R^1$. The perturbation potential $q$ is expressed in terms of the periodic potential $p$ and the scattering data. We also obtain identities for the eigenfunctions of the unperturbed Hill's operator $L_0=-d^2/dx^2+p(x)$. 
@article{MZM_1975_18_6_a4,
     author = {N. E. Firsova},
     title = {An inverse scattering problem for a~perturbed {Hill's} operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {831--843},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a4/}
}
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N. E. Firsova. An inverse scattering problem for a~perturbed Hill's operator. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 831-843. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a4/