A. B. Zheglov, D. V. Osipov, “Lax pairs for linear Hamiltonian systems”, Sibirsk. Mat. Zh., 2019, Volume 60, Number 4,Pages <nobr>760

This article is cited in 3 papers

Lax pairs for linear Hamiltonian systems

A. B. Zheglov^a, D. V. Osipov^bcd

^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.

UDC: 517.926

Received: 11.10.2018
Revised: 11.10.2018
Accepted: 19.12.2018

DOI: 10.33048/smzh.2019.60.405