RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






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


Regul. Chaotic Dyn., 2015, Volume 20, Issue 2, Pages 123–133 (Mi rcd49)  

This article is cited in 7 scientific papers (total in 7 papers)

Analytical Solutions of the Lorenz System

Nikolay A. Kudryashov

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Shosse 31, Moscow, 115409 Russia

Abstract: The Lorenz system is considered. The Painlevé test for the third-order equation corresponding to the Lorenz model at $\sigma \ne 0$ is presented. The integrable cases of the Lorenz system and the first integrals for the Lorenz system are discussed. The main result of the work is the classification of the elliptic solutions expressed via the Weierstrass function. It is shown that most of the elliptic solutions are degenerated and expressed via the trigonometric functions. However, two solutions of the Lorenz system can be expressed via the elliptic functions.

Keywords: Lorenz system, Painlevé property, Painlevé test, analytical solutions, elliptic solutions

Funding Agency Grant Number
Russian Science Foundation 14-11-00258
This research was supported by the Russian Science Foundation grant No. 14-11-00258.


DOI: https://doi.org/10.1134/S1560354715020021

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 01-00, 01A55, 01A60
Received: 08.01.2015
Language: English

Citation: Nikolay A. Kudryashov, “Analytical Solutions of the Lorenz System”, Regul. Chaotic Dyn., 20:2 (2015), 123–133

Citation in format AMSBIB
\Bibitem{Kud15}
\by Nikolay A. Kudryashov
\paper Analytical Solutions of the Lorenz System
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 123--133
\mathnet{http://mi.mathnet.ru/rcd49}
\crossref{https://doi.org/10.1134/S1560354715020021}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3332946}
\zmath{https://zbmath.org/?q=an:1331.34005}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..123K}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000352483000002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928266796}


Linking options:
  • http://mi.mathnet.ru/eng/rcd49
  • http://mi.mathnet.ru/eng/rcd/v20/i2/p123

    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. N. A. Kudryashov, “Refinement of the Korteweg-de Vries equation from the Fermi-Pasta-Ulam model”, Phys. Lett. A, 379:40-41 (2015), 2610–2614  crossref  mathscinet  zmath  isi  scopus
    2. A. K. Volkov, N. A. Kudryashov, “Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system”, Comput. Math. Math. Phys., 56:4 (2016), 680–687  mathnet  crossref  crossref  mathscinet  isi  elib
    3. N. A. Kudryashov, “On solutions of generalized modified Korteweg-de Vries equation of the fifth order with dissipation”, Appl. Math. Comput., 280 (2016), 39–45  crossref  mathscinet  isi  scopus
    4. N. A. Kudryashov, “From the Fermi-Pasta-Ulam model to higher-order nonlinear evolution equations”, Rep. Math. Phys., 77:1 (2016), 57–67  crossref  mathscinet  zmath  isi  scopus
    5. N. A. Kudryashov, Yu. S. Ivanova, “Painlevé analysis and exact solutions for the modified Korteweg-de Vries equation with polynomial source”, Appl. Math. Comput., 273 (2016), 377–382  crossref  mathscinet  isi  scopus
    6. Jaume Llibre, Clàudia Valls, “Darboux Polynomials, Balances and Painlevé Property”, Regul. Chaotic Dyn., 22:5 (2017), 543–550  mathnet  crossref
    7. L. Bougoffa, S. Al-Awfi, S. Bougouffa, “A complete and partial integrability technique of the Lorenz system”, Results Phys., 9 (2018), 712–716  crossref  isi  scopus
  • Number of views:
    This page:119
    References:28

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019