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TMF, 2013, Volume 176, Number 2, Pages 163–188 (Mi tmf8512)  

This article is cited in 13 scientific papers (total in 13 papers)

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

V. M. Buchstaberab, S. I. Tertychnyia

a All-Russian Scientific Research Institute of Physical-Technical and Radiotechnical Measurements, Mendeleevo, Moscow Oblast, Russia
b Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: We obtain and study a family of solutions of the equation $\dot\phi+\sin\phi =B+A\cos\omega t$, 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 $M_{\mathrm P}$ of parameters $(A,B,\omega)$ 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 $(A,B,\omega)\in M_{\mathrm rP}$.

Keywords: dynamical system on a torus, double confluent Heun equations, polynomial solution, rotation number, Poincaré map

DOI: https://doi.org/10.4213/tmf8512

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English version:
Theoretical and Mathematical Physics, 2013, 176:2, 965–986

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Received: 06.02.2013

Citation: V. M. Buchstaber, S. I. Tertychnyi, “Explicit solution family for the equation of the resistively shunted Josephson junction model”, TMF, 176:2 (2013), 163–188; Theoret. and Math. Phys., 176:2 (2013), 965–986

Citation in format AMSBIB
\by V.~M.~Buchstaber, S.~I.~Tertychnyi
\paper Explicit solution family for the~equation of the~resistively shunted Josephson junction model
\jour TMF
\yr 2013
\vol 176
\issue 2
\pages 163--188
\jour Theoret. and Math. Phys.
\yr 2013
\vol 176
\issue 2
\pages 965--986

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    Citing articles on Google Scholar: Russian citations, English citations
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    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.  crossref  mathscinet  isi
    2. A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Mosc. Math. J., 14:2 (2014), 367–384  mathnet  crossref  mathscinet
    3. V. M. Buchstaber, S. I. Tertychnyi, “Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction”, Theoret. and Math. Phys., 182:3 (2015), 329–355  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. V. M. Buchstaber, S. I. Tertychnyi, “On a Remarkable Sequence of Bessel Matrices”, Math. Notes, 98:5 (2015), 714–724  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. M. Buchstaber, S. I. Tertychnyi, “Automorphisms of the solution spaces of special double-confluent Heun equations”, Funct. Anal. Appl., 50:3 (2016), 176–192  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Buchstaber V.M. Glutsyuk A.A., “On determinants of modified Bessel functions and entire solutions of double confluent Heun equations”, Nonlinearity, 29:12 (2016), 3857–3870  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Glutsyuk A.A., “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  crossref  isi
    9. A. V. Malyutin, “The Rotation Number Integer Quantization Effect in Braid Groups”, Proc. Steklov Inst. Math., 305 (2019), 182–194  mathnet  crossref  crossref  mathscinet  isi  elib
    10. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. Tertychniy S.I., “Symmetries of the Space of Solutions to Special Double Confluent Heun Equations of Integer Order”, J. Math. Phys., 60:10 (2019), 103501  crossref  mathscinet  isi
    12. A. E. Artisevich, A. B. Shabat, “Tri teoremy o matritsakh Vandermonda”, Vladikavk. matem. zhurn., 22:1 (2020), 5–12  mathnet  crossref
    13. 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  mathnet  crossref  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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