Siberian Mathematical Journal

, Volume 60, Issue 4, pp 592–604 | Cite as

Lax Pairs for Linear Hamiltonian Systems

  • A. B. ZheglovEmail author
  • D. V. OsipovEmail author


We construct Lax pairs for linear Hamiltonian systems of differential equations. In particular, the Gröbner bases are used for computations. It is proved that the mappings in the construction of Lax pairs are Poisson. Under study are the various properties of first integrals of the system which are obtained from Lax pairs.


Lax pairs linear Hamiltonian systems first integrals Gröbner bases 


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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia
  4. 4.National University of Science and Technology “MISiS,”MoscowRussia

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