RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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, 2012, Volume 172, Number 1, Pages 138–154 (Mi tmf6925)  

This article is cited in 6 scientific papers (total in 6 papers)

Rolling in the Higgs model and elliptic functions

I. Ya. Aref'eva, I. V. Volovich, E. V. Piskovskiy

Steklov Mathematical Institute, Moscow, Russia

Abstract: Asymptotic methods in nonlinear dynamics such as, for example, the Krylov–Bogoliubov averaging method and the KAM theory are commonly used to improve perturbation theory results in the regime of small oscillations. But for a series of problems in nonlinear dynamics, in particular, for the Higgs equation in field theory, not only the small-oscillation regime but also the rolling regime is of interest. Both slow- and fast-rolling regimes are important in the Friedmann cosmology. We present an asymptotic method for solving the Higgs equation in the rolling regime. We show that to improve the perturbation theory in the rolling regime, expanding a solution known in terms of elliptic functions not in trigonometric functions (as with the averaging method in the small-oscillation regime) but in hyperbolic functions turns out to be effective. We estimate the accuracy of the second approximation. We also investigate the Higgs equation with damping.

Keywords: asymptotic methods in nonlinear dynamics, rolling, Higgs model

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00894_a
11-01-00828_a
11-01-12114-офи_м
Ministry of Education and Science of the Russian Federation НШ-4612.2012.1
НШ-2928.2012.1


DOI: https://doi.org/10.4213/tmf6925

Full text: PDF file (571 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2012, 172:1, 1001–1016

Bibliographic databases:

Document Type: Article
Received: 09.02.2012

Citation: I. Ya. Aref'eva, I. V. Volovich, E. V. Piskovskiy, “Rolling in the Higgs model and elliptic functions”, TMF, 172:1 (2012), 138–154; Theoret. and Math. Phys., 172:1 (2012), 1001–1016

Citation in format AMSBIB
\Bibitem{AreVolPis12}
\by I.~Ya.~Aref'eva, I.~V.~Volovich, E.~V.~Piskovskiy
\paper Rolling in the~Higgs model and elliptic functions
\jour TMF
\yr 2012
\vol 172
\issue 1
\pages 138--154
\mathnet{http://mi.mathnet.ru/tmf6925}
\crossref{https://doi.org/10.4213/tmf6925}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3170058}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012TMP...172.1001A}
\elib{http://elibrary.ru/item.asp?id=20732499}
\transl
\jour Theoret. and Math. Phys.
\yr 2012
\vol 172
\issue 1
\pages 1001--1016
\crossref{https://doi.org/10.1007/s11232-012-0091-9}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000307309800009}
\elib{http://elibrary.ru/item.asp?id=20472655}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865593367}


Linking options:
  • http://mi.mathnet.ru/eng/tmf6925
  • https://doi.org/10.4213/tmf6925
  • http://mi.mathnet.ru/eng/tmf/v172/i1/p138

    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. I. Ya. Aref'eva, I. V. Volovich, “Asymptotic expansion of solutions in a rolling problem”, Proc. Steklov Inst. Math., 277 (2012), 1–15  mathnet  crossref  mathscinet  isi
    2. E. V. Piskovskii, “Rezhim skatyvaniya v modeli Khiggsa s treniem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(31) (2013), 127–130  mathnet  crossref  elib
    3. Alimi J.M. Golubtsova A.A. Reverdy V., “Elliptic Solutions of Generalized Brans-Dicke Gravity With a Non-Universal Coupling”, Eur. Phys. J. C, 74:10 (2014), 3125  crossref  adsnasa  isi
    4. Aref'eva I.Ya. Bulatov N.V. Gorbachev R.V. Vernov S.Yu., “Non-Minimally Coupled Cosmological Models With the Higgs-Like Potentials and Negative Cosmological Constant”, Class. Quantum Gravity, 31:6 (2014), 065007  crossref  mathscinet  zmath  adsnasa  isi
    5. A. A. Solovev, “Otsenka ostatochnogo chlena dlya asimptoticheskogo predstavleniya ellipticheskogo sinusa, soderzhaschego tri pervykh chlena razlozheniya”, Tr. IMM UrO RAN, 23, no. 2, 2017, 220–229  mathnet  crossref  elib
    6. A. V. Krasilnikov, “Ob asimptotike ellipticheskogo sinusa”, Chelyab. fiz.-matem. zhurn., 2:2 (2017), 169–180  mathnet  mathscinet  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:538
    Full text:80
    References:32
    First page:39

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018