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Theoretical and Mathematical Physics

, Volume 183, Issue 1, pp 540–552 | Cite as

Scattering theory for delta-type potentials

  • A. B. Shabat
Article

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 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Aliev Karachaev-Cherkess State UniversityKarachaevskRussia
  2. 2.Landau Institute for Theoretical PhysicsRASMoscowRussia

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