  We study scaling properties of energy spreading in disordered strongly
nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled
local linear or nonlinear oscillators, and demonstrate a rather slow,
subdiffusive spreading of initially localized wave p ackets. We use a
fractional nonlinear diffusion equation as a heuristic model of this process,
and confirm that the scaling predictions resulting from a self-similar solution
of this equation are indeed applicable to all studied cases. We s how that the
spreading in nonlinearly coupled linear oscillators slows down compared to a
pure power law, while for nonlinear local oscillators a power law is valid in
the whole studied range of parameters.
