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Funktsional'nyi Analiz i ego Prilozheniya, 2016, Volume 50, Issue 3, Pages 12–33
DOI: https://doi.org/10.4213/faa3245 (Mi faa3245) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Automorphisms of the solution spaces of special double-confluent Heun equations

V. M. Buchstabera, S. I. Tertychnyib

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b All-Russia Research Institute of Physical-Technical and Radiotechnical Measurements (VNIIFTRI), Mendeleevo, Moscow oblast, Russia
Full-text PDF (272 kB) Citations (12)
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DOI: https://doi.org/10.4213/faa3245
Abstract: Two new linear operators determining automorphisms of the solution space of a special double-confluent Heun equation in the general case are obtained. This equation has two singular points, both of which are irregular. The obtained result is applied to solve the nonlinear equation of the resistively shunted junction model for an overdamped Josephson junction in superconductors. The new operators are explicitly expressed in terms of structural polynomials, for which recursive computational algorithms are constructed. Two functional equations for the solutions of the special double-confluent Heun equation are found.
Keywords: special functions, double-confluent Heun equation, solution space, automorphisms, functional equations.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00506
This work was supported in part by the Russian Foundation for Basic Research, project no. 14-01-00506.
Received: 30.03.2016
English version:
Functional Analysis and Its Applications, 2016, Volume 50, Issue 3, Pages 176–192
DOI: https://doi.org/10.1007/s10688-016-0146-z
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. M. Buchstaber, S. I. Tertychnyi, “Automorphisms of the solution spaces of special double-confluent Heun equations”, Funktsional. Anal. i Prilozhen., 50:3 (2016), 12–33; Funct. Anal. Appl., 50:3 (2016), 176–192
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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