  We consider the relation between exact solutions of cosmological models
having minimally and non-minimally coupled scalar fields. This is done for a
particular class of solvable models which, in the Einstein frame, have
potentials depending on hyperbolic functions and in the Jordan frame, where the
non-minimal coupling is conformal, possess a relatively simple dynamics. We
show that a particular model in this class can be generalized to the cases of
closed and open Friedmann universes and still exhibits a simple dynamics.
Further we illustrate the conditions for the existences of bounces in some
sub-classes of the set of integrable models we have considered.
