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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






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


SIGMA, 2012, Volume 8, 090, 37 pages (Mi sigma767)  

This article is cited in 4 scientific papers (total in 4 papers)

The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$

Mariya N. Kuznetsovaa, Asli Pekcanb, Anatoliy V. Zhiberc

a Ufa State Aviation Technical University, 12 K. Marx Str., Ufa, Russia
b Department of Mathematics, Istanbul University, Istanbul, Turkey
c Ufa Institute of Mathematics, Russian Academy of Science, 112 Chernyshevskii Str., Ufa, Russia

Abstract: We present the complete classification of equations of the form $u_{xy} = f(u, u_x, u_y)$ and the Klein–Gordon equations $v_{xy} = F(v)$ connected with one another by differential substitutions $v = \varphi(u, u_x, u_y)$ such that $\varphi_{u_x}\varphi_{u_y}\neq 0$ over the ring of complex-valued variables.

Keywords: Klein–Gordon equation; differential substitution

DOI: https://doi.org/10.3842/SIGMA.2012.090

Full text: PDF file (552 kB)
Full text: http://emis.mi.ras.ru/.../090
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1111.7255
MSC: 35L70
Received: April 25, 2012; in final form November 14, 2012; Published online November 26, 2012
Language:

Citation: Mariya N. Kuznetsova, Asli Pekcan, Anatoliy V. Zhiber, “The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$”, SIGMA, 8 (2012), 090, 37 pp.

Citation in format AMSBIB
\Bibitem{KuzPekZhi12}
\by Mariya~N.~Kuznetsova, Asli~Pekcan, Anatoliy~V.~Zhiber
\paper The Klein--Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$
\jour SIGMA
\yr 2012
\vol 8
\papernumber 090
\totalpages 37
\mathnet{http://mi.mathnet.ru/sigma767}
\crossref{https://doi.org/10.3842/SIGMA.2012.090}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3007269}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312378800001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84881618264}


Linking options:
  • http://mi.mathnet.ru/eng/sigma767
  • http://mi.mathnet.ru/eng/sigma/v8/p90

    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. V. Chrastinova, V. Tryhuk, “On the internal approach to differential equations. 1. The involutiveness and standard basis”, Math. Slovaca, 66:4 (2016), 999–1018  crossref  mathscinet  zmath  isi  scopus
    2. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.  mathnet  crossref
    3. Sakovich S.Yu., “On a New Avatar of the Sine-Gordon Equation”, Nonlinear Phenom. Complex Syst., 21:1 (2018), 62–68  zmath  isi
    4. S. Ya. Startsev, “Zakony sokhraneniya dlya giperbolicheskikh uravnenii: lokalnyi algoritm poiska proobraza otnositelno polnoi proizvodnoi”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 85–92  mathnet
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:175
    Full text:41
    References:15

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