  We construct so called Darboux matrices and fundamental solutions in the
important case of the generalised Hamiltonian (or canonical) systems depending
rationally on the spectral parameter. A wide class of explicit solutions is
obtained in this way. Interesting results for dynamical systems depending on
several variables and their explicit solutions follow. For these purposes we
use our version of B\"acklund-Darboux transformation and square roots of the
corresponding generalised matrix eigenvalues. Some new auxiliary results on the
roots of matrices are included as well. An appendix is added to make the paper
self-sufficient.
