RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 10 scientific papers (total in 10 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

Full text: PDF file (638 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{BucTer13}
\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
\mathnet{http://mi.mathnet.ru/tmf8512}
\crossref{https://doi.org/10.4213/tmf8512}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3230400}
\zmath{https://zbmath.org/?q=an:1291.34002}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013TMP...176..965B}
\elib{http://elibrary.ru/item.asp?id=20732645}
\transl
\jour Theoret. and Math. Phys.
\yr 2013
\vol 176
\issue 2
\pages 965--986
\crossref{https://doi.org/10.1007/s11232-013-0085-2}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000324094000001}
\elib{http://elibrary.ru/item.asp?id=20455475}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884160303}


Linking options:
  • http://mi.mathnet.ru/eng/tmf8512
  • https://doi.org/10.4213/tmf8512
  • http://mi.mathnet.ru/eng/tmf/v176/i2/p163

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Mosc. Math. J., 14:2 (2014), 367–384  mathnet  crossref  mathscinet
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. A. V. Malyutin, “The Rotation Number Integer Quantization Effect in Braid Groups”, Proc. Steklov Inst. Math., 305 (2019), 182–194  mathnet  crossref  crossref  isi  elib
    9. 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  adsnasa  isi  elib
    10. A. E. Artisevich, A. B. Shabat, “Tri teoremy o matritsakh Vandermonda”, Vladikavk. matem. zhurn., 22:1 (2020), 5–12  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:656
    Full text:130
    References:45
    First page:37

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020