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, 2007, Volume 153, Number 1, Pages 29–45 (Mi tmf6119)  

This article is cited in 13 scientific papers (total in 13 papers)

Model equation of the theory of solitons

V. E. Adler, A. B. Shabat

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We consider the hierarchy of integrable $(1+2)$-dimensional equations related to the Lie algebra of vector fields on the line. We construct solutions in quadratures that contain $n$ arbitrary functions of a single argument. A simple equation for the generating function of the hierarchy, which determines the dynamics in negative times and finds applications to second-order spectral problems, is of main interest. Considering its polynomial solutions under the condition that the corresponding potential is regular allows developing a rather general theory of integrable $(1+1)$-dimensional equations.

Keywords: hierarchy of commuting vector fields, Riemann invariant, Dubrovin equations

DOI: https://doi.org/10.4213/tmf6119

Full text: PDF file (492 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2007, 153:1, 1373–1387

Bibliographic databases:

Received: 29.01.2007

Citation: V. E. Adler, A. B. Shabat, “Model equation of the theory of solitons”, TMF, 153:1 (2007), 29–45; Theoret. and Math. Phys., 153:1 (2007), 1373–1387

Citation in format AMSBIB
\Bibitem{AdlSha07}
\by V.~E.~Adler, A.~B.~Shabat
\paper Model equation of the~theory of solitons
\jour TMF
\yr 2007
\vol 153
\issue 1
\pages 29--45
\mathnet{http://mi.mathnet.ru/tmf6119}
\crossref{https://doi.org/10.4213/tmf6119}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2402234}
\zmath{https://zbmath.org/?q=an:1138.37044}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2007TMP...153.1373A}
\elib{http://elibrary.ru/item.asp?id=9918146}
\transl
\jour Theoret. and Math. Phys.
\yr 2007
\vol 153
\issue 1
\pages 1373--1387
\crossref{https://doi.org/10.1007/s11232-007-0121-1}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000250783100003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35448982352}


Linking options:
  • http://mi.mathnet.ru/eng/tmf6119
  • https://doi.org/10.4213/tmf6119
  • http://mi.mathnet.ru/eng/tmf/v153/i1/p29

    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. Burovskiy P.A., Ferapontov E.V., Tsarev S.P., “Second-order quasilinear PDEs and conformal structures in projective space”, Internat. J. Math., 21:6 (2010), 799–841  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. B. Shabat, “Simmetricheskie mnogochleny i zakony sokhraneniya”, Vladikavk. matem. zhurn., 14:4 (2012), 83–94  mathnet
    3. A. B. Shabat, “Rational interpolation and solitons”, Theoret. and Math. Phys., 179:3 (2014), 637–648  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Morozov O.I., Sergyeyev A., “The Four-Dimensional Martinez Alonso-Shabat Equation: Reductions and Nonlocal Symmetries”, J. Geom. Phys., 85 (2014), 40–45  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Pavlov M.V., “Integrable Dispersive Chains and Energy Dependent Schrodinger Operator”, J. Phys. A-Math. Theor., 47:29 (2014), 295204  crossref  mathscinet  zmath  isi  scopus
    6. Ferapontov E.V., Moss J., “Characteristic Integrals in 3D and Linear Degeneracy”, J. Nonlinear Math. Phys., 21:2 (2014), 214–224  crossref  mathscinet  isi  scopus
    7. Baran H., Krasil'shchik I.S., Morozov O.I., Vojcak P., “Symmetry Reductions and Exact Solutions of Lax Integrable 3-Dimensional Systems”, J. Nonlinear Math. Phys., 21:4 (2014), 643–671  crossref  mathscinet  isi  scopus
    8. Ferapontov E.V., Moss J., “Linearly Degenerate Partial Differential Equations and Quadratic Line Complexes”, Commun. Anal. Geom., 23:1 (2015), 91–127  crossref  mathscinet  zmath  isi  scopus
    9. Morozov O.I., Pavlov M.V., “Backlund Transformations Between Four Lax-Integrable 3D Equations”, J. Nonlinear Math. Phys., 24:4 (2017), 465–468  crossref  mathscinet  isi  scopus
    10. Lelito A., Morozov O.I., “Three-Component Nonlocal Conservation Laws For Lax-Integrable 3D Partial Differential Equations”, J. Geom. Phys., 131 (2018), 89–100  crossref  mathscinet  zmath  isi  scopus
    11. H. Baran, I. S. Krasil'shchik, O. I. Morozov, P. Vojčák, “Nonlocal symmetries of integrable linearly degenerate equations: A comparative study”, Theoret. and Math. Phys., 196:2 (2018), 1089–1110  mathnet  crossref  crossref  adsnasa  isi  elib
    12. F. Calogero, “Zeros of entire functions and related systems of infinitely many nonlinearly coupled evolution equations”, Theoret. and Math. Phys., 196:2 (2018), 1111–1128  mathnet  crossref  crossref  adsnasa  isi  elib
    13. Marvan M., Pavlov M.V., “Integrable Dispersive Chains and Their Multi-Phase Solutions”, Lett. Math. Phys., 109:5 (2019), 1219–1245  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:700
    Full text:269
    References:87
    First page:10

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