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

V. M. Buchstaber, S. I. Tertychnyi

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)176-192
Number of pages17
JournalFunctional Analysis and its Applications
Volume50
Issue number3
DOIs
Publication statusPublished - 1 Jul 2016
Externally publishedYes

Keywords

  • automorphisms
  • double-confluent Heun equation
  • functional equations
  • solution space
  • special functions

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