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Teoreticheskaya i Matematicheskaya Fizika, 1990, Volume 85, Number 3, Pages 368–375 (Mi tmf5955)  

This article is cited in 27 scientific papers (total in 27 papers)

Invertible changes of variables generated by Bäcklund transformations

R. I. Yamilov
References:
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.
Received: 08.06.1990
English version:
Theoretical and Mathematical Physics, 1990, Volume 85, Issue 2, Pages 1269–1275
DOI: https://doi.org/10.1007/BF01018403
Bibliographic databases:
Language: Russian
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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\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 85
\issue 2
\pages 1269--1275
\crossref{https://doi.org/10.1007/BF01018403}
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Linking options:
  • https://www.mathnet.ru/eng/tmf5955
  • https://www.mathnet.ru/eng/tmf/v85/i3/p368
  • This publication is cited in the following 27 articles:
    1. S Ya Startsev, “Darboux integrability of hyperbolic partial differential equations: is it a property of integrals rather than equations?”, J. Phys. A: Math. Theor., 58:2 (2025), 025206  crossref
    2. R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of fifth-order symmetries”, Theoret. and Math. Phys., 222:1 (2025), 10–19  mathnet  crossref  crossref
    3. V. E. Adler, “3D consistency of negative flows”, Theoret. and Math. Phys., 221:2 (2024), 1836–1851  mathnet  crossref  crossref  adsnasa
    4. R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of third-order symmetries”, Theoret. and Math. Phys., 217:2 (2023), 1767–1776  mathnet  crossref  crossref  mathscinet  adsnasa
    5. S. Ya. Startsev, “On Bäcklund Transformations Preserving the Darboux Integrability of Hyperbolic Equations”, Lobachevskii J Math, 44:5 (2023), 1929  crossref
    6. Ufa Math. J., 13:2 (2021), 107–114  mathnet  crossref  isi
    7. R. N. Garifullin, “On integrability of semi-discrete Tzitzeica equation”, Ufa Math. J., 13:2 (2021), 15–21  mathnet  crossref  isi
    8. Ufa Math. J., 13:2 (2021), 160–169  mathnet  crossref  isi
    9. Garifullin R.N. Habibullin I.T., “Generalized Symmetries and Integrability Conditions For Hyperbolic Type Semi-Discrete Equations”, J. Phys. A-Math. Theor., 54:20 (2021), 205201  crossref  isi
    10. R. N. Garifullin, R. I. Yamilov, “Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure”, Theoret. and Math. Phys., 205:1 (2020), 1264–1278  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. 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
    12. Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.  mathnet  crossref
    13. Ufa Math. J., 11:3 (2019), 99–108  mathnet  crossref  isi
    14. 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
    15. R N Garifullin, I T Habibullin, R I Yamilov, “Peculiar symmetry structure of some known discrete nonautonomous equations”, J. Phys. A: Math. Theor., 48:23 (2015), 235201  crossref
    16. Sergey Ya. Startsev, “Non-Point Invertible Transformations and Integrability of Partial Difference Equations”, SIGMA, 10 (2014), 066, 13 pp.  mathnet  crossref  mathscinet
    17. S. Ya. Startsev, “Integriruemye po Darbu differentsialno-raznostnye uravneniya, dopuskayuschie integral pervogo poryadka”, Ufimsk. matem. zhurn., 4:3 (2012), 161–176  mathnet
    18. 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
    19. 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
    20. 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
    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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