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

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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.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    V. M. Buchstaber

  2. All-Russia Research Institute of Physical-Technical and Radiotechnical Measurements (VNIIFTRI), Mendeleevo, Moscow oblast, Russia

    S. I. Tertychnyi

Authors
  1. V. M. Buchstaber
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  2. S. I. Tertychnyi
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Correspondence to V. M. Buchstaber.

Additional information

Translated from Funktsional 1 nyi Analiz i Ego Prilozheniya, Vol. 50, No. 3, pp. 12–33, 2016 Original Russian Text Copyright © by V. M. Buchstaber and S. I. Tertychnyi

This work was supported in part by the Russian Foundation for Basic Research, project no. 14-01-00506.

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Buchstaber, V.M., Tertychnyi, S.I. Automorphisms of the solution spaces of special double-confluent Heun equations. Funct Anal Its Appl 50, 176–192 (2016). https://doi.org/10.1007/s10688-016-0146-z

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  • DOI: https://doi.org/10.1007/s10688-016-0146-z

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