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TMF, 2005, Volume 142, Number 1, Pages 13–20 (Mi tmf1759)  

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

A class of integrable evolutionary vector equations

M. Yu. Balakhnev

Orel State University

Abstract: We present the results of classifying integrable evolutionary $N$-component vector equations and construct Bäcklund transformations for each equation as proof of the exact integrability.

Keywords: vector evolutionary equations, Bäcklund transformations

DOI: https://doi.org/10.4213/tmf1759

Full text: PDF file (187 kB)
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English version:
Theoretical and Mathematical Physics, 2005, 142:1, 8–14

Bibliographic databases:

Received: 06.04.2004
Revised: 05.05.2004

Citation: M. Yu. Balakhnev, “A class of integrable evolutionary vector equations”, TMF, 142:1 (2005), 13–20; Theoret. and Math. Phys., 142:1 (2005), 8–14

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Anatoly G. Meshkov, Maxim Ju. Balakhnev, “Integrable Anisotropic Evolution Equations on a Sphere”, SIGMA, 1 (2005), 027, 11 pp.  mathnet  crossref  mathscinet  zmath
    2. A. G. Meshkov, “On symmetry classification of third order evolutionary systems of divergent type”, J. Math. Sci., 151:4 (2008), 3167–3181  mathnet  crossref  mathscinet  zmath
    3. M. Yu. Balakhnev, “Superposition Formulas for Vector Generalizations of the mKdV Equation”, Math. Notes, 82:4 (2007), 448–450  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. M. Yu. Balakhnev, “Superposition formulas for integrable vector evolution equations”, Theoret. and Math. Phys., 154:2 (2008), 220–226  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Anatoly G.G. Meshkov, Maxim Ju. Balakhnev, “Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions”, SIGMA, 4 (2008), 018, 29 pp.  mathnet  crossref  mathscinet  zmath
    6. Balakhnev M.Ju., Meshkov A.G., “On a classification of integrable vectorial evolutionary equations”, J. Nonlinear Math. Phys., 15:2 (2008), 212–226  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. Balakhnev M.Ju., “Superposition formulas for integrable vector evolutionary equations on a sphere”, J. Nonlinear Math. Phys., 15:1 (2008), 104–116  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    8. M. Yu. Balakhnev, A. G. Meshkov, “Integrable vector evolution equations admitting zeroth-order conserved densities”, Theoret. and Math. Phys., 164:2 (2010), 1002–1007  mathnet  crossref  crossref  zmath  adsnasa  isi
    9. 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
    10. Balakhnev M.Ju., “New examples of the auto-Backlund transformations and nonlinear superposition formulas for vector evolution systems”, Phys. Lett. A, 375:3 (2011), 529–536  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    11. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    12. M. Yu. Balakhnev, “Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order”, Math. Notes, 94:3 (2013), 307–313  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. Meshkov A., Sokolov V., “Vector Hyperbolic Equations on the Sphere Possessing Integrable Third-Order Symmetries”, Lett. Math. Phys., 104:3 (2014), 341–360  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. M. Yu. Balakhnev, “Differential Substitutions for Vectorial Generalizations of the mKdV Equation”, Math. Notes, 98:2 (2015), 204–209  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Meshkov A.G. Sokolov V.V., “On third order integrable vector Hamiltonian equations”, J. Geom. Phys., 113 (2017), 206–214  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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