Nonlinear waves in disordered chains: probing the limits of chaos and spreading

TL;DR

This paper investigates the behavior of nonlinear wave spreading in disordered chains, demonstrating that chaos-driven spreading persists asymptotically even under strong disorder and in models with inhomogeneous nonlinearity.

Contribution

It extends previous studies by analyzing the limits of wave spreading under strong disorder and in specific models, confirming the persistence of chaos-driven spreading.

Findings

Chaotic wave packet dynamics align with all studied cases.

Wave spreading appears asymptotic without slowing down.

Inhomogeneous nonlinearity models support the main conclusions.

Abstract

We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [EPL {\bf 91}, 30001 (2010)] and consider strong disorder, which favors Anderson localization. We probe the limit of infinite disorder strength and study Fr\"ohlich-Spencer-Wayne models. We find that the assumption of chaotic wave packet dynamics and its impact on spreading is in accord with all studied cases. Spreading appears to be asymptotic, without any observable slowing down. We also consider chains with spatially inhomogeneous nonlinearity which give further support to our findings and conclusions.