RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






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


TMF, 1998, Volume 116, Number 3, Pages 336–348 (Mi tmf907)  

This article is cited in 14 scientific papers (total in 14 papers)

Differential substitutions of the Miura transformation type

S. Ya. Startsev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: The existence of a nontrivial integral and a sufficiently large set of symmetries with respect to one of the characteristics of a hyperbolic equation implies the existence of nontrivial integrals and symmetries with respect to the other characteristic. We classify differential substitutions of the form $w=P(x,u,u_{x})$ relating families of evolution equations that depend on an arbitrary function. Among such substitutions, there are infinitely many pairwise-nonequivalent ones.

DOI: https://doi.org/10.4213/tmf907

Full text: PDF file (242 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1998, 116:3, 1001–1010

Bibliographic databases:

Received: 16.04.1998

Citation: S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, TMF, 116:3 (1998), 336–348; Theoret. and Math. Phys., 116:3 (1998), 1001–1010

Citation in format AMSBIB
\Bibitem{Sta98}
\by S.~Ya.~Startsev
\paper Differential substitutions of the Miura transformation type
\jour TMF
\yr 1998
\vol 116
\issue 3
\pages 336--348
\mathnet{http://mi.mathnet.ru/tmf907}
\crossref{https://doi.org/10.4213/tmf907}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1693881}
\zmath{https://zbmath.org/?q=an:0948.35012}
\elib{http://elibrary.ru/item.asp?id=13288194}
\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 116
\issue 3
\pages 1001--1010
\crossref{https://doi.org/10.1007/BF02557141}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000078007000002}


Linking options:
  • http://mi.mathnet.ru/eng/tmf907
  • https://doi.org/10.4213/tmf907
  • http://mi.mathnet.ru/eng/tmf/v116/i3/p336

    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. S. Ya. Startsev, “Laplace invariants of hyperbolic equations linearizable by a differential substitution”, Theoret. and Math. Phys., 120:2 (1999), 1009–1018  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. V. Zhiber, S. Ya. Startsev, “Integrals, Solutions, and Existence Problems for Laplace Transformations of Linear Hyperbolic Systems”, Math. Notes, 74:6 (2003), 803–811  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. K. Demskoi, “One Class of Liouville-Type Systems”, Theoret. and Math. Phys., 141:2 (2004), 1509–1527  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. V. M. Zhuravlev, “The method of generalized Cole–Hopf substitutions and new examples of linearizable nonlinear evolution equations”, Theoret. and Math. Phys., 158:1 (2009), 48–60  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. M. Yu. Balakhnev, “First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$”, Math. Notes, 89:2 (2011), 184–193  mathnet  crossref  crossref  mathscinet  isi
    8. 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
    9. S. Ya. Startsev, “Integriruemye po Darbu differentsialno-raznostnye uravneniya, dopuskayuschie integral pervogo poryadka”, Ufimsk. matem. zhurn., 4:3 (2012), 161–176  mathnet
    10. Startsev S.Ya., “Darboux Integrable Discrete Equations Possessing An Autonomous First-Order Integral”, J. Phys. A-Math. Theor., 47:10 (2014), 105204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    11. 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
    12. 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
    13. S. Ya. Startsev, “On differential substitutions for evolution systems”, Ufa Math. J., 9:4 (2017), 108–113  mathnet  crossref  isi  elib
    14. Startsev S.Ya., “Relationships Between Symmetries Depending on Arbitrary Functions and Integrals of Discrete Equations”, J. Phys. A-Math. Theor., 50:50 (2017), 50LT01  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:427
    Full text:127
    References:32
    First page:2

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