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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 122, Number 1, Pages 50–57
DOI: https://doi.org/10.4213/tmf554 (Mi tmf554) 		 
This article is cited in 8 scientific papers (total in 8 papers)

An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$

E. I. Ganzha

Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev
Full-text PDF (227 kB) Citations (8)
DOI: https://doi.org/10.4213/tmf554
Abstract: We present a new Bäcklund-type transformation for the nonlinear equation $\theta_{xy}=2\sqrt{\lambda(x,y)\theta_x\theta_y}$ studied by É. Goursat. Goursat found a linearization transformation and some properties of this equation, which make it similar to the Moutard equation $u_{xy}=M(x,y)u$. However, this Goursat transformation does not provide proper superposition formulas. We give the necessary extended superposition formulas.
English version:
Theoretical and Mathematical Physics, 2000, Volume 122, Issue 1, Pages 39–45
DOI: https://doi.org/10.1007/BF02551168
Bibliographic databases:
Language: Russian
Citation: E. I. Ganzha, “An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$”, TMF, 122:1 (2000), 50–57; Theoret. and Math. Phys., 122:1 (2000), 39–45
Citation in format AMSBIB
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\by E.~I.~Ganzha
\paper An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$
\jour TMF
\yr 2000
\vol 122
\issue 1
\pages 50--57
\mathnet{http://mi.mathnet.ru/tmf554}
\crossref{https://doi.org/10.4213/tmf554}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1776506}
\zmath{https://zbmath.org/?q=an:0967.35006}
\elib{https://elibrary.ru/item.asp?id=13346694}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 122
\issue 1
\pages 39--45
\crossref{https://doi.org/10.1007/BF02551168}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000086224200005}
Linking options:
  • https://www.mathnet.ru/eng/tmf554
  • https://doi.org/10.4213/tmf554
  • https://www.mathnet.ru/eng/tmf/v122/i1/p50
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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