Geodesic
On~the~problem of electron density profile reconstruction for layered plasma
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 503-526.

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There are thin areas in frequency domain near quasi-resonance levels where the reflection coefficient changes considerably when the potential is large and nonmonotonic; only quite far from these areas and critical frequencies the WKB approach is satisfactory. When the potential grows then these areas become more and more thin (exponentially) so it is impossible to observe all the resonances and to get the full information about the potential. The nonuniqueness of the inverse problem arises. On the other hand if the parameters of all resonances are known then the reconstruction of nonmonotonic profiles is possible. The approximate methods are proposed for solving forward and inverse problems. 
@article{FPM_1999_5_2_a8,
     author = {V. E. Kunitsyn and I. A. Nesterov},
     title = {On~the~problem of electron density profile reconstruction for layered plasma},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {503--526},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a8/}
}
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V. E. Kunitsyn; I. A. Nesterov. On~the~problem of electron density profile reconstruction for layered plasma. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 503-526. http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a8/