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Mat. Zametki, 2006, Volume 79, Issue 2, Pages 267–277 (Mi mz2694)  

This article is cited in 2 scientific papers (total in 2 papers)

The Heun Equation and the Darboux Transformation

Yu. N. Sirotaa, A. O. Smirnovb

a Herzen State Pedagogical University of Russia
b Saint-Petersburg State University of Aerospace Instrumentation

Abstract: 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.

DOI: https://doi.org/10.4213/mzm2694

Full text: PDF file (241 kB)
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English version:
Mathematical Notes, 2006, 79:2, 244–253

Bibliographic databases:

UDC: 517.912+517.923
Received: 08.07.2004

Citation: Yu. N. Sirota, A. O. Smirnov, “The Heun Equation and the Darboux Transformation”, Mat. Zametki, 79:2 (2006), 267–277; Math. Notes, 79:2 (2006), 244–253

Citation in format AMSBIB
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\paper The Heun Equation and the Darboux Transformation
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Brezhnev, “Elliptic solitons, Fuchsian equations, and algorithms”, St. Petersburg Math. J., 24:4 (2013), 555–574  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Leroy C., Ishkhanyan A.M., “Expansions of the Solutions of the Confluent Heun Equation in Terms of the Incomplete Beta and the Appell Generalized Hypergeometric Functions”, Integral Transform. Spec. Funct., 26:6 (2015), 451–459  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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