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Scattering theory for delta-type potentials

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In memory of S. I. Pohozhaev

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.

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Authors and Affiliations

  1. Aliev Karachaev-Cherkess State University, Karachaevsk, Russia

    A. B. Shabat

  2. Landau Institute for Theoretical Physics, RAS, Moscow, Russia

    A. B. Shabat

Authors
  1. A. B. Shabat
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Correspondence to A. B. Shabat.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 183, No. 1, pp. 105–119, April, 2015.

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Shabat, A.B. Scattering theory for delta-type potentials. Theor Math Phys 183, 540–552 (2015). https://doi.org/10.1007/s11232-015-0280-4

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  • DOI: https://doi.org/10.1007/s11232-015-0280-4

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