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Theoretical and Mathematical Physics

, Volume 173, Issue 2, pp 1507–1517 | Cite as

Two-sided Darboux transformations

  • A. B. Shabat
  • Z. S. Élkanova
  • A. B. Urusova
Article

Abstract

We refine the notion of a Darboux transformation for differential operators of an order higher than two and consider commutative rings of differential operators that are invariant under the group of dilations of the independent variable.

Keywords

Darboux transformation commutative ring of differential operators third-order Bessel equation 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • A. B. Shabat
    • 1
    • 2
  • Z. S. Élkanova
    • 1
  • A. B. Urusova
    • 1
  1. 1.Aliev Karachaev-Cherkess State UniversityKarachaevskRussia
  2. 2.Landau Institute for Theoretical PhysicsRASChernogolovka, Moscow OblastRussia

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