This article is cited in 4 papers

Scattering theory for delta-type potentials

A. B. Shabat<sup>ab

a</sup> Landau Institute for Theoretical Physics, RAS, Moscow, Russia
^b Aliev Karachaev-Cherkess State University, Karachaevsk, Russia

Abstract: 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.

Received: 25.08.2014

DOI: 10.4213/tmf8783

 English version: Theoretical and Mathematical Physics, 2015, 183:1, 540–552

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