Email this article Automorphisms of the solution spaces of special double-confluent Heun equations
- Authors: Buchstaber V.M.1, Tertychnyi S.I.2
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- All-Russia Research Institute of Physical-Technical and Radiotechnical Measurements (VNIIFTRI)
- Issue: Vol 50, No 3 (2016)
- Pages: 176-192
- Section: Article
- URL: https://journals.rcsi.science/0016-2663/article/view/234199
- DOI: https://doi.org/10.1007/s10688-016-0146-z
- ID: 234199
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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.
About the authors
V. M. Buchstaber
Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: buchstab@mi.ras.ru
Russian Federation, Moscow
S. I. Tertychnyi
All-Russia Research Institute of Physical-Technical and Radiotechnical Measurements (VNIIFTRI)
Email: buchstab@mi.ras.ru
Russian Federation, Mendeleevo, Moscow oblast
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