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We observe a crossover from strong to weak chaos in the spatiotemporalevolution of multiple site excitations within disordered chains with cubicnonlinearity. Recent studies have shown that Anderson localization isdestroyed, and the wave packet spreading is characterized by an asymptoticdivergence of the second moment $m_2$ in time (as $t^{1/3}$), due to weakchaos. In the present paper, we observe the existence of a qualitatively newdynamical regime of strong chaos, in which the second moment spreads evenfaster (as $t^{1/2}$), with a crossover to the asymptotic law of weak chaos atlarger times. We analyze the pecularities of these spreading regimes andperform extensive numerical simulations over large times with ensembleaveraging. A technique of local derivatives on logarithmic scales is developedin order to quantitatively visualize the slow crossover processes.

The crossover from strong to weak chaos for nonlinear waves in disordered systems