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 Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 3, Pages 12–33 (Mi faa3245)

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

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.

DOI: https://doi.org/10.4213/faa3245

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English version:
Functional Analysis and Its Applications, 2016, 50:3, 176–192

Bibliographic databases:

UDC: 517.9

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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• http://mi.mathnet.ru/eng/faa3245
• https://doi.org/10.4213/faa3245
• http://mi.mathnet.ru/eng/faa/v50/i3/p12

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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. Glutsyuk A.A., Netay I.V., “On Spectral Curves and Complexified Boundaries of the Phase-Lock Areas in a Model of Josephson Junction”, J. Dyn. Control Syst.
2. V. M. Buchstaber, A. A. Glutsyuk, “On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect”, Proc. Steklov Inst. Math., 297 (2017), 50–89
3. V. M. Buchstaber, S. I. Tertychnyi, “Representations of the Klein Group Determined by Quadruples of Polynomials Associated with the Double Confluent Heun Equation”, Math. Notes, 103:3 (2018), 357–371
4. A. A. Glutsyuk, “On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation”, J. Dyn. Control Syst., 25:3 (2019), 323–349
5. A. V. Malyutin, “The Rotation Number Integer Quantization Effect in Braid Groups”, Proc. Steklov Inst. Math., 305 (2019), 182–194
6. S. I. Tertychnyi, “Solution space monodromy of a special double confluent Heun equation and its applications”, Theoret. and Math. Phys., 201:1 (2019), 1426–1441
7. S. I. Tertychniy, “Symmetries of the space of solutions to special double confluent Heun equations of integer order”, J. Math. Phys., 60:10 (2019), 103501
8. V. M. Buchstaber, S. I. Tertychnyi, “Group algebras acting on the space of solutions of a special double confluent Heun equation”, Theoret. and Math. Phys., 204:2 (2020), 967–983
9. I S. Tertychniy, “Square root of the monodromy map associated with the equation of rsj model of Josephson junction”, Results Math., 75:4 (2020), 139
10. V. M. Buchstaber, S. I. Tertychnyi, “Categories of Symmetry Groups of the Space of Solutions of the Special Doubly Confluent Heun Equation”, Math. Notes, 110:5 (2021), 643–654
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