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TMF, 1994, Volume 100, Number 2, Pages 214–218 (Mi tmf1642)  

This article is cited in 30 scientific papers (total in 30 papers)

Vector-matrix generalizations of classical integrable equations

S. I. Svinolupov, V. V. Sokolov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: Some vector-matrix generalizations, both known and new, for well-known integrable equations are presented. All of them possess higher symmetries and conservation laws.

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English version:
Theoretical and Mathematical Physics, 1994, 100:2, 959–962

Bibliographic databases:

Received: 23.04.1993

Citation: S. I. Svinolupov, V. V. Sokolov, “Vector-matrix generalizations of classical integrable equations”, TMF, 100:2 (1994), 214–218; Theoret. and Math. Phys., 100:2 (1994), 959–962

Citation in format AMSBIB
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\paper Vector-matrix generalizations of classical integrable equations
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\jour Theoret. and Math. Phys.
\yr 1994
\vol 100
\issue 2
\pages 959--962
\crossref{https://doi.org/10.1007/BF01016758}
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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, V. V. Sokolov, “Deformations of triple Jordan systems and integrable equations”, Theoret. and Math. Phys., 108:3 (1996), 1160–1163  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. 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
    3. I. Z. Golubchik, V. V. Sokolov, “Integrable equations on $\mathbb Z$-graded Lie algebras”, Theoret. and Math. Phys., 112:3 (1997), 1097–1103  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Olver, PJ, “Integrable evolution equations on associative algebras”, Communications in Mathematical Physics, 193:2 (1998), 245  crossref  mathscinet  zmath  adsnasa  isi
    5. I. Z. Golubchik, V. V. Sokolov, “Generalized Heisenberg equations on $\mathbb Z$-graded Lie algebras”, Theoret. and Math. Phys., 120:2 (1999), 1019–1025  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. I. Z. Golubchik, V. V. Sokolov, “Multicomponent generalization of the hierarchy of the Landau–Lifshitz equation”, Theoret. and Math. Phys., 124:1 (2000), 909–917  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Golubchik, IZ, “Generalized operator Yang–Baxter equations, integrable ODEs and nonassociative algebras”, Journal of Nonlinear Mathematical Physics, 7:2 (2000), 184  crossref  mathscinet  zmath  adsnasa  isi
    8. 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
    9. Meshkov, AG, “Integrable evolution equations on the N-dimensional sphere”, Communications in Mathematical Physics, 232:1 (2002), 1  crossref  mathscinet  zmath  adsnasa  isi
    10. D. K. Demskoi, A. G. Meshkov, “Lax Representation for a Triplet of Scalar Fields”, Theoret. and Math. Phys., 134:3 (2003), 351–364  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Demskoi, DK, “Zero-curvature representation for a chiral-type three-field system”, Inverse Problems, 19:3 (2003), 563  crossref  mathscinet  zmath  adsnasa  isi
    12. 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
    13. 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
    14. Tsuchida, T, “Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I”, Journal of Physics A-Mathematical and General, 38:35 (2005), 7691  crossref  mathscinet  zmath  adsnasa  isi
    15. 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
    16. 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
    17. Sergyeyev, A, “Sasa-Satsuma (complex modified Korteweg-de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more”, Journal of Mathematical Physics, 48:4 (2007), 042702  crossref  mathscinet  zmath  adsnasa  isi
    18. 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
    19. Balakhnev, MJ, “On a classification of integrable vectorial evolutionary equations”, Journal of Nonlinear Mathematical Physics, 15:2 (2008), 212  crossref  mathscinet  zmath  adsnasa  isi
    20. Adler, VE, “Classification of integrable Volterra-type lattices on the sphere: isotropic case”, Journal of Physics A-Mathematical and Theoretical, 41:14 (2008), 145201  crossref  mathscinet  zmath  adsnasa  isi
    21. V. M. Zhuravlev, “The method of generalized Cole–Hopf substitutions and new examples of linearizable nonlinear evolution equations”, Theoret. and Math. Phys., 158:1 (2009), 48–60  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. 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
    23. Gerdjikov V.S., Grahovski G.G., “Two Soliton Interactions of BD.I Multicomponent NLS Equations and Their Gauge Equivalent”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1301, 2010, 561–572  isi
    24. 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
    25. Gerdjikov V.S., “On Soliton Interactions of Vector Nonlinear Schrodinger Equations”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1404, 2011  isi
    26. Balakhnev M.J., “The Vector Ito-Drienfel'd-Sokolov System: Bilinear Backlund Transformation and Lax pair”, J Phys Soc Japan, 80:4 (2011), 045002  crossref  isi
    27. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    28. 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
    29. Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold, “Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart”, SIGMA, 12 (2016), 087, 17 pp.  mathnet  crossref
    30. V. Fenchenko, E. Khruslov, “Nonlinear dynamics of solitons for the vector modified Korteweg–de Vries equation”, Zhurn. matem. fiz., anal., geom., 14:2 (2018), 153–168  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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