Scattering properties of solitons in nonlinear disordered chains

The scattering of a soliton from a disordered one-dimensional atomic lattice with nonlinear nearest-neighbor interactions of quartic type is studied numerically. The disorder is of the binary-alloy type with the concentration of the impurity masses $m$ given by $p$. We numerically find that for large enough lengths $L$, the soliton transmission coefficient $T$ decays as $\frac{1}{\sqrt{L}}$. This behavior has been obtained also by an analytical study of the transmission of a Gaussian wave packet in a linear disordered system. For short and intermediate lengths, $T$ decays with a different power law for different nonlinear potentials. This behavior can be accounted by a simple independent scattering picture. Finally, the role of the boundary conditions in disordered nonlinear systems is discussed.