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TMF, 1991, Volume 87, Number 3, Pages 391–403 (Mi tmf5498)  

This article is cited in 15 scientific papers (total in 15 papers)

Jordan algebras and generalized Korteweg–de Vries equations

S. I. Svinolupov


Abstract: Integrability criteria for many-field Korteweg–de Vries equations are obtained. A one-to-one correspondence between such equations and Jordan algebras is established. It is shown that the so-called irreducible systems correspond to simple Jordan algebras.

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English version:
Theoretical and Mathematical Physics, 1991, 87:3, 611–620

Bibliographic databases:

Received: 21.11.1990

Citation: S. I. Svinolupov, “Jordan algebras and generalized Korteweg–de Vries equations”, TMF, 87:3 (1991), 391–403; Theoret. and Math. Phys., 87:3 (1991), 611–620

Citation in format AMSBIB
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\by S.~I.~Svinolupov
\paper Jordan algebras and generalized Korteweg--de~Vries equations
\jour TMF
\yr 1991
\vol 87
\issue 3
\pages 391--403
\mathnet{http://mi.mathnet.ru/tmf5498}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1129673}
\zmath{https://zbmath.org/?q=an:0746.35044}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 87
\issue 3
\pages 611--620
\crossref{https://doi.org/10.1007/BF01017947}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GW78600003}


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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. I. Svinolupov, “Jordan Algebras and Integrable Systems”, Funct. Anal. Appl., 27:4 (1993), 257–265  mathnet  crossref  mathscinet  zmath  isi
    2. S. I. Svinolupov, V. V. Sokolov, “Vector-matrix generalizations of classical integrable equations”, Theoret. and Math. Phys., 100:2 (1994), 959–962  mathnet  crossref  mathscinet  zmath  isi
    3. S. I. Svinolupov, I. T. Habibullin, “Integrable boundary conditions for many-component burgers equations”, Math. Notes, 60:6 (1996), 671–680  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Olver, PJ, “Integrable evolution equations on associative algebras”, Communications in Mathematical Physics, 193:2 (1998), 245  crossref  mathscinet  zmath  adsnasa  isi
    5. Gurses, M, “On construction of recursion operators from Lax representation”, Journal of Mathematical Physics, 40:12 (1999), 6473  crossref  mathscinet  adsnasa  isi
    6. Sokolov, VV, “Classification of integrable polynomial vector evolution equations”, Journal of Physics A-Mathematical and General, 34:49 (2001), 11139  crossref  mathscinet  zmath  adsnasa  isi
    7. Meshkov, AG, “Integrable evolution equations on the N-dimensional sphere”, Communications in Mathematical Physics, 232:1 (2002), 1  crossref  mathscinet  zmath  adsnasa  isi
    8. A. G. Meshkov, V. V. Sokolov, “Classification of Integrable Divergent $N$-Component Evolution Systems”, Theoret. and Math. Phys., 139:2 (2004), 609–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Balakhnev, MJ, “On a classification of integrable vectorial evolutionary equations”, Journal of Nonlinear Mathematical Physics, 15:2 (2008), 212  crossref  mathscinet  zmath  adsnasa  isi
    10. Ziemowit Popowicz, “The Integrability of New Two-Component KdV Equation”, SIGMA, 6 (2010), 018, 10 pp.  mathnet  crossref  mathscinet
    11. Wang D.-Shan, “Integrability of a coupled KdV system: Painlevé property, Lax pair and Backlund transformation”, Applied Mathematics and Computation, 216:4 (2010), 1349–1354  crossref  isi
    12. A. V. Zhiber, R. D. Murtazina, I. T. Khabibullin, A. B. Shabat, “Kharakteristicheskie koltsa Li i integriruemye modeli matematicheskoi fiziki”, Ufimsk. matem. zhurn., 4:3 (2012), 17–85  mathnet  mathscinet
    13. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    14. I. T. Habibullin, A. R. Khakimova, “A direct algorithm for constructing recursion operators and Lax pairs for integrable models”, Theoret. and Math. Phys., 196:2 (2018), 1200–1216  mathnet  crossref  crossref  adsnasa  isi  elib
    15. Habibullin I.T. Khakimova A.R., “On the Recursion Operators For Integrable Equations”, J. Phys. A-Math. Theor., 51:42 (2018), 425202  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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