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TMF, 2004, Volume 139, Number 2, Pages 192–208 (Mi tmf55)  

This article is cited in 19 scientific papers (total in 19 papers)

Classification of Integrable Divergent $N$-Component Evolution Systems

A. G. Meshkova, V. V. Sokolovb

a Orel State University
b Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Abstract: We use a symmetry approach to solve the classification problem for integrable $N$-component evolution systems having the form of conservation laws. We obtain complete lists of both isotropic and anisotropic systems of this type and find auto-Bдcklund transformations with a spectral parameter for all systems.

Keywords: symmetries, Bäcklund transformation, evolution equations

DOI: https://doi.org/10.4213/tmf55

Full text: PDF file (275 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 139:2, 609–622

Bibliographic databases:

Received: 22.04.2003
Revised: 21.05.2003

Citation: A. G. Meshkov, V. V. Sokolov, “Classification of Integrable Divergent $N$-Component Evolution Systems”, TMF, 139:2 (2004), 192–208; Theoret. and Math. Phys., 139:2 (2004), 609–622

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. M. Yu. Balakhnev, “A class of integrable evolutionary vector equations”, Theoret. and Math. Phys., 142:1 (2005), 8–14  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Balakhnev MJ, “The vector generalization of the Landau-Lifshitz equation: Backlund transformation and solutions”, Applied Mathematics Letters, 18:12 (2005), 1363–1372  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Anatoly G. Meshkov, Maxim Ju. Balakhnev, “Integrable Anisotropic Evolution Equations on a Sphere”, SIGMA, 1 (2005), 027, 11 pp.  mathnet  crossref  mathscinet  zmath
    4. 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
    5. 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
    6. 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
    7. Balakhnev, MJ, “On a classification of integrable vectorial evolutionary equations”, Journal of Nonlinear Mathematical Physics, 15:2 (2008), 212  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Adler, VE, “On vector analogs of the modified Volterra lattice”, Journal of Physics A-Mathematical and Theoretical, 41:45 (2008), 455203  crossref  zmath  adsnasa  isi  scopus  scopus
    9. Balakhnev, MJ, “Superposition formulas for integrable vector evolutionary equations on a sphere”, Journal of Nonlinear Mathematical Physics, 15:1 (2008), 104  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Adler, VE, “Classification of integrable Volterra-type lattices on the sphere: isotropic case”, Journal of Physics A-Mathematical and Theoretical, 41:14 (2008), 145201, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    11. A. G. Meshkov, “Vector hyperbolic equations with higher symmetries”, Theoret. and Math. Phys., 161:2 (2009), 1471–1484  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. 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
    13. 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
    14. 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
    15. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    16. 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
    17. 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
    18. 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
    19. 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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