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TMF, 1985, Volume 62, Number 1, Pages 3–29 (Mi tmf4527)  

This article is cited in 15 scientific papers (total in 17 papers)

Local and nonlocal currents for nonlinear equations

V. S. Vladimirov, I. V. Volovich


Abstract: A general method is suggested for constructing conserving currents for a wide class of (many-dimensional) nonlinear equations. For nonlinear differential equations which can be presented as conditions of solvability of some over-determined linear system with a parameter (in particular, for the equations integrable by means of the inverse scattering transform method), the procedure of the explicit evaluation of conserving currents is proposed.

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English version:
Theoretical and Mathematical Physics, 1985, 62:1, 1–20

Bibliographic databases:

Document Type: Article
Received: 11.07.1984

Citation: V. S. Vladimirov, I. V. Volovich, “Local and nonlocal currents for nonlinear equations”, TMF, 62:1 (1985), 3–29; Theoret. and Math. Phys., 62:1 (1985), 1–20

Citation in format AMSBIB
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\by V.~S.~Vladimirov, I.~V.~Volovich
\paper Local and nonlocal currents for nonlinear equations
\jour TMF
\yr 1985
\vol 62
\issue 1
\pages 3--29
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=782097}
\zmath{https://zbmath.org/?q=an:0566.35090}
\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 62
\issue 1
\pages 1--20
\crossref{https://doi.org/10.1007/BF01034820}
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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. V. S. Vladimirov, I. V. Volovich, “Conservation laws for non-linear equations”, Russian Math. Surveys, 40:4 (1985), 13–24  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. V. Volovich, “Supersymmetric chiral field with anomaly and its integrability”, Theoret. and Math. Phys., 63:2 (1985), 533–535  mathnet  crossref  mathscinet  isi
    3. V. V. Zharinov, “Conservation laws of evolution systems”, Theoret. and Math. Phys., 68:2 (1986), 745–751  mathnet  crossref  mathscinet  zmath  isi
    4. V. A. Andreev, “Odd bases of Lie superalgebras and integrable equations”, Theoret. and Math. Phys., 72:1 (1987), 758–764  mathnet  crossref  mathscinet  zmath  isi
    5. F. Kh. Mukminov, “On straightening the characteristics of a quasilinear second-order equation”, Theoret. and Math. Phys., 75:1 (1988), 340–345  mathnet  crossref  mathscinet  zmath  isi
    6. E. V. Doktorov, M. V. Milovanov, “Connection between the Einstein–Maxwell equations and the self-duality equations for gauge fields”, Theoret. and Math. Phys., 75:3 (1988), 599–604  mathnet  crossref  mathscinet  isi
    7. V. A. Yatsun, “Quasiself-dual fields in $N=4$ supersymmetric Yang–Mills theory”, Theoret. and Math. Phys., 77:3 (1988), 1239–1247  mathnet  crossref  mathscinet  isi
    8. V. V. Zharinov, “Extrinsic geometry of differential equations and Green's formula”, Math. USSR-Izv., 35:1 (1990), 37–60  mathnet  crossref  mathscinet  zmath
    9. V. V. Zharinov, “String symmetries and conservation laws”, Theoret. and Math. Phys., 81:2 (1989), 1125–1133  mathnet  crossref  mathscinet  zmath  isi
    10. S. P. Novikov, “Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory”, Funct. Anal. Appl., 24:4 (1990), 296–306  mathnet  crossref  mathscinet  zmath  isi
    11. F. A. Lunev, “Analog of Noether's theorem for non-Noether and nonlocal symmetries”, Theoret. and Math. Phys., 84:2 (1990), 816–820  mathnet  crossref  mathscinet  isi
    12. A. A. Gonchar, G. I. Marchuk, S. P. Novikov, “Vasilii Sergeevich Vladimirov (on his seventieth birthday)”, Russian Math. Surveys, 48:1 (1993), 201–212  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    14. M. O. Katanaev, “Prostoe dokazatelstvo adiabaticheskoi teoremy”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 99–107  mathnet  crossref  elib
    15. I. V. Volovich, V. Zh. Sakbaev, “Universal boundary value problem for equations of mathematical physics”, Proc. Steklov Inst. Math., 285 (2014), 56–80  mathnet  crossref  crossref  isi
    16. M. O. Katanaev, “Geometricheskie metody v matematicheskoi fizike. Prilozheniya v kvantovoi mekhanike. Chast 1”, Lekts. kursy NOTs, 25, MIAN, M., 2015, 3–174  mathnet  crossref  elib
    17. M. O. Katanaev, “Geometricheskie metody v matematicheskoi fizike. Prilozheniya v kvantovoi mekhanike. Chast 2”, Lekts. kursy NOTs, 26, MIAN, M., 2015, 3–184  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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