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Uspekhi Mat. Nauk, 1988, Volume 43, Issue 5(263), Pages 133–163 (Mi umn1977)  

This article is cited in 43 scientific papers (total in 43 papers)

On the symmetries of evolution equations

V. V. Sokolov

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English version:
Russian Mathematical Surveys, 1988, 43:5, 165–204

Bibliographic databases:

UDC: 517.95
MSC: 46H10, 46J30
Received: 23.03.1987

Citation: V. V. Sokolov, “On the symmetries of evolution equations”, Uspekhi Mat. Nauk, 43:5(263) (1988), 133–163; Russian Math. Surveys, 43:5 (1988), 165–204

Citation in format AMSBIB
\by V.~V.~Sokolov
\paper On the symmetries of evolution equations
\jour Uspekhi Mat. Nauk
\yr 1988
\vol 43
\issue 5(263)
\pages 133--163
\jour Russian Math. Surveys
\yr 1988
\vol 43
\issue 5
\pages 165--204

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    This publication is cited in the following articles:
    1. S. I. Svinolupov, V. V. Sokolov, “Representations of contragradient Lie algebras in contact vector fields”, Funct. Anal. Appl., 25:2 (1991), 146–147  mathnet  crossref  mathscinet  zmath  isi
    2. S. I. Svinolupov, V. V. Sokolov, “Factorization of evolution equations”, Russian Math. Surveys, 47:3 (1992), 127–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. L Abellanas, C Martinez Ontalba, J Phys A Math Gen, 26:23 (1993), L1229  crossref  mathscinet  zmath  adsnasa  isi
    4. A Gonzalez-Lopez, J Phys A Math Gen, 27:4 (1994), 1205  crossref  mathscinet  zmath  adsnasa  isi
    5. S. I. Svinolupov, V. V. Sokolov, “Vector-matrix generalizations of classical integrable equations”, Theoret. and Math. Phys., 100:2 (1994), 959–962  mathnet  crossref  mathscinet  zmath  isi
    6. V. V. Sokolov, S. I. Svinolupov, “On nonclassical invertible transformations of hyperbolic equations”, Eur J Appl Math, 6:2 (1995)  crossref  mathscinet
    7. Rafael Hernández Heredero, Peter J. Olver, “Classification of invariant wave equations”, J Math Phys (N Y ), 37:12 (1996), 6414  crossref  mathscinet  zmath  isi
    8. 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
    9. S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, Theoret. and Math. Phys., 116:3 (1998), 1001–1010  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Arthur Sergheyev, “Generalized symmetries of partial differential equations and quasi-exact solvability”, Reports on Mathematical Physics, 41:3 (1998), 279  crossref
    11. V V Sokolov, Thomas Wolf, Inverse Probl, 15:2 (1999), L5  crossref  mathscinet  zmath  adsnasa  isi
    12. Artur Sergyeyev, “On symmetries of KdV-like evolution equations”, Reports on Mathematical Physics, 44:1-2 (1999), 183  crossref
    13. A Sergyeyev, J Phys A Math Gen, 34:23 (2001), 4983  crossref  mathscinet  zmath  adsnasa  isi
    14. A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Russian Math. Surveys, 56:1 (2001), 61–101  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. R. Hernandez Heredero, “Integrable Quasilinear Equations”, Theoret. and Math. Phys., 133:2 (2002), 1516–1528  mathnet  crossref  crossref  mathscinet  isi
    16. Artur Sergyeyev, “On sufficient conditions of locality for hierarchies of symmetries of evolution systems”, Reports on Mathematical Physics, 50:3 (2002), 307  crossref
    17. M Gürses, A Karasu, R Turhan, “Time-Dependent Recursion Operators and Symmetries”, Journal of Nonlinear Mathematical Physics, 9:2 (2002), 210  crossref
    18. Artur Sergyeyev, Jan A Sanders, “A Remark on Nonlocal Symmetries for the Calogero–Degasperis–Ibragimov–Shabat Equation”, Journal of Nonlinear Mathematical Physics, 10:1 (2003), 78  crossref
    19. D. K. Demskoi, “One Class of Liouville-Type Systems”, Theoret. and Math. Phys., 141:2 (2004), 1509–1527  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. A Sergyeyev, “Why nonlocal recursion operators produce local symmetries: new results and applications”, J Phys A Math Gen, 38:15 (2005), 3397  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. Hynek Baran, “Can we always distinguish between positive and negative hierarchies?”, J Phys A Math Gen, 38:18 (2005), L301  crossref  mathscinet  zmath  isi
    22. Ravil Yamilov, “Symmetries as integrability criteria for differential difference equations”, J Phys A Math Gen, 39:45 (2006), R541  crossref  mathscinet  zmath  isi
    23. Demskoi, D, “On application of Liouville type equations to constructing Backlund transformations”, Journal of Nonlinear Mathematical Physics, 14:1 (2007), 147  crossref  mathscinet  zmath  adsnasa  isi
    24. Artur Sergyeyev, “Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility”, SIGMA, 3 (2007), 062, 14 pp.  mathnet  crossref  mathscinet  zmath
    25. V.N. Grebenev, M. Oberlack, “Compatible differential constraints to an infinite chain of transport equations for cumulants”, Communications in Nonlinear Science and Numerical Simulation, 12:3 (2007), 336  crossref
    26. 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
    27. Renat Zhdanov, “On relation between potential and contact symmetries of evolution equations”, J Math Phys (N Y ), 50:5 (2009), 053522  crossref  mathscinet  zmath  isi  elib
    28. Renat Zhdanov, “Nonlocal symmetries of evolution equations”, Nonlinear Dyn, 2009  crossref  isi
    29. A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. Qing Huang, Changzheng Qu, Renat Zhdanov, “Group-theoretical framework for potential symmetries of evolution equations”, J. Math. Phys, 52:2 (2011), 023514  crossref  elib
    31. Maciej Dunajski, Vladimir Sokolov, “On the 7th order ODE with submaximal symmetry”, Journal of Geometry and Physics, 61:8 (2011), 1258  crossref
    32. S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufa Math. J., 3:1 (2011), 78–82  mathnet  zmath
    33. M. S. Bruzón, M. L. Gandarias, “Classical and nonclassical symmetries for the Krichever–Novikov equation”, Theoret. and Math. Phys., 168:1 (2011), 875–885  mathnet  crossref  crossref  mathscinet  adsnasa
    34. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    35. S. Ya. Startsev, “Integriruemye po Darbu differentsialno-raznostnye uravneniya, dopuskayuschie integral pervogo poryadka”, Ufimsk. matem. zhurn., 4:3 (2012), 161–176  mathnet
    36. Mariya N. Kuznetsova, Asli Pekcan, Anatoliy V. Zhiber, “The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$”, SIGMA, 8 (2012), 090, 37 pp.  mathnet  crossref  mathscinet
    37. José del Amor, Ángel Giménez, Pascual Lucas, “A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms”, Journal of Geometry and Physics, 2014  crossref
    38. V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, Theoret. and Math. Phys., 181:2 (2014), 1367–1382  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    39. Jiřina Vodová-Jahnová, “On symmetries and conservation laws of the Majda–Biello system”, Nonlinear Analysis: Real World Applications, 22 (2015), 148  crossref
    40. Qing Huang, Renat Zhdanov, “Group classification of nonlinear evolution equations: semi-simple groups of contact transformations”, Communications in Nonlinear Science and Numerical Simulation, 2015  crossref
    41. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.  mathnet  crossref
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    43. Demskoi D.K., “Factorisation of Recursion Operators of Some Lagrangian Systems”, J. Nonlinear Math. Phys., 24:3 (2017), 368–378  crossref  isi
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