Numerical methods for non-linear diffusion

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I have the following non-linear diffusion equation, for $\ z(x,t)$:

$\ z_t = -C\sin^m(\omega t) \,x^{hm}\left[hm x^{-1}(z_x)^n + n z_{xx} (z_x)^{n-1}\right]$

Any advice for numerical (or analytical) solutions?