Geodesic
Scattering theory for delta-type potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 105-119

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In the example of the Korteweg–de Vries equation, we consider the problem of extending the applicability of the inverse spectral transform method using delta-type potentials and their Darboux transformations. In this case, the problem of the properties of scattering data reduces to studying explicitly given entire functions of the spectral parameter.
Keywords: inverse spectral problem, additional spectrum, Korteweg–de Vries equation, second Painlevé equation. 
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     author = {A. B. Shabat},
     title = {Scattering theory for delta-type potentials},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_1_a6/}
}
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A. B. Shabat. Scattering theory for delta-type potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 105-119. http://geodesic.mathdoc.fr/item/TMF_2015_183_1_a6/