Lax Pairs for Linear Hamiltonian Systems
Mathematical Physics
2019-11-26 v1 Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Abstract
In the paper Lax pairs for linear Hamiltonian systems of differential equations are constructed. In particular, Gr\"obner 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.
Cite
@article{arxiv.1901.11130,
title = {Lax Pairs for Linear Hamiltonian Systems},
author = {D. V. Osipov and A. B. Zheglov},
journal= {arXiv preprint arXiv:1901.11130},
year = {2019}
}
Comments
18 p., to appear in Sib. Mat. J