Explicit solution family for the equation of the resistively shunted Josephson junction model

V. M. Buchstaber, S. I. Tertychniy

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We obtain and study a family of solutions of the equation φ + sin φ {symbol} = B + A cos ωt, which is applicable to several problems in physics, mechanics, and geometry. We use polynomial solutions of double confluent Heun equations associated with this equation to construct the family. We describe the manifold MP of parameters (A,B, ω) of these solutions and obtain explicit formulas for the rotation number and Poincaré map of the dynamical system on a torus corresponding to this equation with parameters (A,B, ω) ∈ MP.

Original languageEnglish
Pages (from-to)965-986
Number of pages22
JournalTheoretical and Mathematical Physics
Volume176
Issue number2
DOIs
Publication statusPublished - Aug 2013
Externally publishedYes

Keywords

  • double confluent Heun equations
  • dynamical system on a torus
  • Poincaré map
  • polynomial solution
  • rotation number

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