  Owing to the analogy between the Connes-Kreimer theory of the renormalization
and the integrable systems, we derive the differential equations of the unit
mass for the renormalized character $\phi_+$ and the counter term $\phi_-$. We
give another proof for the scattering type formula of $\phi_-$. The
differential equation of the counter term of coordinate on ${\mathbb P}^1$ is
also given. The hierarchy of the renormalization groups is defined as the
integrable systems.
