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We study the spreading of single-site excitations in one-dimensionaldisordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{\sigma}u_{l}$ for different values of $\sigma$. We perform extensive numericalsimulations where wave packets are evolved a) without and, b) with dephasing innormal mode space. Subdiffusive spreading is observed with the second moment ofwave packets growing as $t^{\alpha}$. The dependence of the numericallycomputed exponent $\alpha$ on $\sigma$ is in very good agreement with ourtheoretical predictions both for the evolution of the wave packet with andwithout dephasing (for $\sigma \geq 2$ in the latter case). We discuss evidenceof the existence of a regime of strong chaos, and observe destruction ofAnderson localization in the packet tails for small values of $\sigma$.

Spreading of wave packets in disordered systems with tunable nonlinearity