  An analytical method of electromagnetic wave interactions with a general
radially anisotropic cloak is established. It is able to deal with arbitrary
parameters ($\epsilon_r(r)$, $\mu_r(r)$, $\epsilon_t(r)$ and $\mu_t(r)$) of a
radially anisotropic inhomogeneous shell. The general cloaking condition is
proposed from the wave relations for the first time. We derive the parameters
of a novel class of spherical nonlinear cloaks and examine its invisibility
performance by the proposed method at various nonlinear situations. Spherical
metamaterial cloaks with improved invisibility performance is achieved with
optimal nonlinearity in transformation and core-shell ratio.
