Lax pairs for linear Hamiltonian systems. (English. Russian original) Zbl 1427.37046

Sib. Math. J. 60, No. 4, 592-604 (2019); translation from Sib. Mat. Zh. 60, No. 4, 760-776 (2019).
Summary: 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.


37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37J06 General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants
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