Lax Pairs for Linear Hamiltonian Systems
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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.
KeywordsLax pairs linear Hamiltonian systems first integrals Gröbner bases
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