  We present results on the relationships between persistent currents and the
known conservation laws in the classical Toda ring. We also show that
perturbing the integrability leads to a decay of the currents at long times,
with a time scale that is determined by the perturbing parameter. We summarize
several known results concerning the Toda ring in 1-dimension, and present new
results relating to the frequency, average kinetic and potential energy, and
mean square displacement in the cnoidal waves, as functions of the wave vector
and a parameter that determines the non linearity.
