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Article

Пары Лакса для линейных гамильтоновых систем

Жеглов А. Б., Осипов Д. В.

In the paper, Lax pairs for linear Hamiltonian systems of differential equations are constructed. In particular, Groebner bases are used for the computations. It is proved that the maps which appear in the construction of Lax pairs are Poisson. Various properties of first integrals of the system which are obtained from  the Lax pairs are investigated.