Anderson localization and solitonic energy transport in one-dimensional oscillatory systems

In a harmonically disordered chain with a regular array of quartic nearest-neighbor anharmonicity we have found a constructive or conflicting interplay of Anderson localization and solitary solutions depending on the type of initial excitation (momentum or displacement). In the present work we specifically discuss energy propagation ensuing after the momentum excitation of a single mass. A coexistence of Anderson localization and superdiffusive energy transport is found. Further, it is found that disorder destabilizes the supersonic solitary solution, whereas conversely anharmonicity reduces Anderson localization. A detailed analysis is given.