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Sibirsk. Mat. Zh., 2019, Volume 60, Number 4, Pages 760–776 (Mi smj3113)  

This article is cited in 2 scientific papers (total in 2 papers)

Lax pairs for linear Hamiltonian systems

A. B. Zheglova, D. V. Osipovbcd

a Lomonosov Moscow State University, Moscow, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
c National Research University Higher School of Economics, Moscow, Russia
d National University of Science and Technology “MISiS”, Moscow, Russia

Abstract: 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.

Keywords: Lax pairs, linear Hamiltonian systems, first integrals, Gröbner bases.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00378_а
16-51-55012_ГФЕН_а
Ministry of Education and Science of the Russian Federation 14.641.31.0001
The first author was supported by the Russian Foundation for Basic Research (Grants 16-01-00378a and 16-51-55012 China-a). The second author was partially supported by the Laboratory of Mirror Symmetry NRU HSE (RF Government Grant, Ag. No. 14.641.31.0001).


DOI: https://doi.org/10.33048/smzh.2019.60.405

Full text: PDF file (471 kB)
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English version:
Siberian Mathematical Journal, 2019, 60:4, 592–604

Bibliographic databases:

UDC: 517.926
Received: 11.10.2018
Revised: 11.10.2018
Accepted:19.12.2018

Citation: A. B. Zheglov, D. V. Osipov, “Lax pairs for linear Hamiltonian systems”, Sibirsk. Mat. Zh., 60:4 (2019), 760–776; Siberian Math. J., 60:4 (2019), 592–604

Citation in format AMSBIB
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\by A.~B.~Zheglov, D.~V.~Osipov
\paper Lax pairs for linear Hamiltonian systems
\jour Sibirsk. Mat. Zh.
\yr 2019
\vol 60
\issue 4
\pages 760--776
\mathnet{http://mi.mathnet.ru/smj3113}
\crossref{https://doi.org/10.33048/smzh.2019.60.405}
\elib{http://elibrary.ru/item.asp?id=41623689}
\transl
\jour Siberian Math. J.
\yr 2019
\vol 60
\issue 4
\pages 592--604
\crossref{https://doi.org/10.1134/S0037446619040050}
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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. V. V. Kozlov, “Quadratic conservation laws for equations of mathematical physics”, Russian Math. Surveys, 75:3 (2020), 445–494  mathnet  crossref  crossref  isi
    2. V. V. Kozlov, “The Liouville Equation as a Hamiltonian System”, Math. Notes, 108:3 (2020), 339–343  mathnet  crossref  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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