Russian Journal of Mathematical Physics

, Volume 22, Issue 2, pp 201–214 | Cite as

Integrable Hamiltonian equations of fifth order with Hamiltonian operator D x



All nonequivalent integrable evolution equations of the fifth order of the form \(u_t = D_x \tfrac{{\delta H}} {{\delta u}}\) are found.


Mathematical Physic Integrability Condition Canonical Transformation Hamiltonian Operator Hamiltonian Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. G. Meshkov and V. V. Sokolov, “Integrable Evolution Hamiltonian Equations of the Third Order with the Hamiltonian Operator D x,” J. Geom. Phys. 85, 245–251 (2014).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    V. V. Sokolov and A. B. Shabat, “Classification of Integrable Evolution Equations,” Sov. Sci. Rev., Sect. C Math. Phys. Rev. 4, 221–280 (1984).MathSciNetGoogle Scholar
  3. 3.
    A. V. Mikhailov, V. V. Sokolov, and A. B. Shabat, “The Symmetry Approach to Classification of Integrable Equations,” What is Integrability? V.E. Zakharov, ed. Springer series in Nonlinear Dynamics, 115–184 (1991).CrossRefGoogle Scholar
  4. 4.
    J. A. Sanders and J. P. Wang, “On the Integrability of Homogeneous Scalar Evolution Equations,” J. Differential Equations 147, 410–434 (1998).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    P. Olver and J. P. Wang, “Classification of Integrable One-Component Systems on Associative Algebras,” Proc. London Math. Soc. 81(3), 566–586 (2000).MathSciNetCrossRefGoogle Scholar
  6. 6.
    P. J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1986).CrossRefGoogle Scholar
  7. 7.
    A. G. Meshkov and V. V. Sokolov, “Integrable Evolution Equations with Constant Separant,” Ufim. Math. J. 4(3), 104–154 (2012) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.State University ESPCOrelRussia
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

Personalised recommendations