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 equationDarboux transformationDarboux-Treibich-Verdier equationlinear ordinary differential equations of second orderthe Schrodinger operatorBessel 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