Symmetry, Integrability and Geometry: Methods and Applications
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

Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 063, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.063 (Mi sigma91) 		 
This article is cited in 23 scientific papers (total in 23 papers)

The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients

Tadashi Kobayashia, Kouichi Todab

a High-Functional Design G, LSI IP Development Div., ROHM CO., LTD., 21, Saiin Mizosaki-cho, Ukyo-ku, Kyoto 615-8585, Japan
b Department of Mathematical Physics, Toyama Prefectural University, Kurokawa 5180, Imizu, Toyama, 939-0398, Japan
Full-text PDF (867 kB) Citations (23)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2006.063
Abstract: The general KdV equation (gKdV) derived by T. Chou is one of the famous $(1+1)$ dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation, which is integrable in the sense of the Painlevé test, is presented. A transformation that links this equation to the canonical form of the Calogero–Bogoyavlenskii–Schiff equation is found. Furthermore, the form and similar transformation for the higher-dimensional modified gKdV equation are also obtained.
Keywords: KdV equation with variable-coefficients; Painlevé test; higher-dimensional integrable systems.
Received: November 30, 2005; in final form June 17, 2006; Published online June 30, 2006
Bibliographic databases:
Document Type: Article
MSC: 37K10; 35Q53
Language: English
Citation: Tadashi Kobayashi, Kouichi Toda, “The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients”, SIGMA, 2 (2006), 063, 10 pp.
Citation in format AMSBIB
\Bibitem{KobTod06}
\by Tadashi Kobayashi, Kouichi Toda
\paper The Painlev\'e Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with
Variable-Coefficients
\jour SIGMA
\yr 2006
\vol 2
\papernumber 063
\totalpages 10
\mathnet{http://mi.mathnet.ru/sigma91}
\crossref{https://doi.org/10.3842/SIGMA.2006.063}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2240736}
\zmath{https://zbmath.org/?q=an:1134.37358}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000207065100062}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889234806}
Linking options:
  • https://www.mathnet.ru/eng/sigma91
  • https://www.mathnet.ru/eng/sigma/v2/p63
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:338
    Full-text PDF :79
    References:40
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024