  Dynamics of a quantum system can be described by coupled Heisenberg
equations. In a generic many-body system these equations form an exponentially
large hierarchy that is intractable without approximations. In contrast, in an
integrable system a small subset of operators can be closed with respect to
commutation with the Hamiltonian. As a result, the Heisenberg equations for
these operators can form a smaller closed system amenable to an analytical
treatment. We demonstrate that this indeed happens in a class of integrable
models where the Hamiltonian is an element of the Onsager algebra. We
explicitly solve the system of Heisenberg equations for operators from this
algebra. Two specific models are considered as examples: the transverse field
Ising model and the superintegrable chiral 3-state Potts model.
