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TMF, 1990, Volume 85, Number 3, Pages 368–375 (Mi tmf5955)  

This article is cited in 9 scientific papers (total in 9 papers)

Invertible changes of variables generated by Bäcklund transformations

R. I. Yamilov


Abstract: In the classification of partial differential equations, one cannot avoid the use of invertible changes of variables, which include not only the long-known point and contact transformations but also, for example, so-called symmetric and generalized contact transformations (reviewed by Mikhailov, Shabat, and Yamilov [1]). The present paper considers a further class of invertible changes of variables.

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English version:
Theoretical and Mathematical Physics, 1990, 85:2, 1269–1275

Bibliographic databases:

Received: 08.06.1990

Citation: R. I. Yamilov, “Invertible changes of variables generated by Bäcklund transformations”, TMF, 85:3 (1990), 368–375; Theoret. and Math. Phys., 85:2 (1990), 1269–1275

Citation in format AMSBIB
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\by R.~I.~Yamilov
\paper Invertible changes of~variables generated by~B\"acklund transformations
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\yr 1990
\vol 85
\issue 3
\pages 368--375
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1099132}
\zmath{https://zbmath.org/?q=an:0726.35117}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 85
\issue 2
\pages 1269--1275
\crossref{https://doi.org/10.1007/BF01018403}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990FV76600003}


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    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. S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, Theoret. and Math. Phys., 116:3 (1998), 1001–1010  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. E. Adler, A. B. Shabat, “Dressing chain for the acoustic spectral problem”, Theoret. and Math. Phys., 149:1 (2006), 1324–1337  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Yamilov, R, “Symmetries as integrability criteria for differential difference equations”, Journal of Physics A-Mathematical and General, 39:45 (2006), R541  crossref  mathscinet  zmath  adsnasa  isi
    5. S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufa Math. J., 3:1 (2011), 78–82  mathnet  zmath
    6. S. Ya. Startsev, “Integriruemye po Darbu differentsialno-raznostnye uravneniya, dopuskayuschie integral pervogo poryadka”, Ufimsk. matem. zhurn., 4:3 (2012), 161–176  mathnet
    7. Sergey Ya. Startsev, “Non-Point Invertible Transformations and Integrability of Partial Difference Equations”, SIGMA, 10 (2014), 066, 13 pp.  mathnet  crossref  mathscinet
    8. Garifullin R.N. Yamilov R.I. Levi D., “Non-invertible transformations of differential–difference equations”, J. Phys. A-Math. Theor., 49:37 (2016), 37LT01  crossref  mathscinet  zmath  isi  elib  scopus
    9. Garifullin R.N. Gubbiotti G. Yamilov I R., “Integrable Discrete Autonomous Quad-Equations Admitting, as Generalized Symmetries, Known Five-Point Differential-Difference Equations”, J. Nonlinear Math. Phys., 26:3 (2019), 333–357  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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