  Nonlinear resonant structures consisting of coupled ring resonators can be
modeled by difference-differential equations that take into account
non-instantaneous Kerr response and the effect of loss. We present a simple and
efficient numerical formalism for solution of the system and calculation of the
time evolution. The technique is demonstrated by investigating the dynamical
behavior of the coupled structure with two rings, namely, focusing on
self-pulsing solutions. The influence of both, loss and non-instantaneous Kerr
response, is also presented.
