Mathematical Notes

, Volume 79, Issue 1, pp 244–253

The Heun Equation and the Darboux Transformation

  • Yu. N. Sirota
  • A. O. Smirnov

DOI: 10.1007/s11006-006-0027-5

Cite this article as:
Sirota, Y.N. & Smirnov, A.O. Math Notes (2006) 79: 244. doi:10.1007/s11006-006-0027-5


In this paper, we study the Darboux transformation of the Darboux-Treibich-Verdier equation. On the basis of this transformation, we construct a generalization of the Darboux transformation to the case of the Heun equation and to other linear ordinary differential equations of second order. Examples are given.

Key words

Heun equation Darboux transformation Darboux-Treibich-Verdier equation linear ordinary differential equations of second order the Schrodinger operator Bessel equation 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yu. N. Sirota
    • 1
  • A. O. Smirnov
    • 2
  1. 1.A. I. Gertsen Russian State Pedagogical UniversityRussia
  2. 2.St. Petersburg State University of Aerospace EngineeringSt. PetersburgRussia

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