Nonlinear Anderson localization in Toda lattices

TL;DR

This paper investigates how nonlinearity and randomness in Toda lattices influence Anderson localization, revealing that nonlinearity enhances localization and that soliton interactions are key to understanding this phenomenon.

Contribution

It demonstrates that nonlinearity enhances Anderson localization in Toda lattices and links the effect to soliton formation, expanding understanding of localization in nonlinear systems.

Findings

Random inductance induces Anderson localization in voltage propagation.

Nonlinearity enhances the degree of Anderson localization.

Localization is understood through attractive interactions forming solitons.

Abstract

We study the Anderson localization in nonlinear systems by taking a nonlinear transmission line realizing the Toda lattice. It is found that the randomness in inductance induces the Anderson localization in the voltage propagation. Furthermore, the nonlinearity enhances the Anderson localization. They are understood in terms of attractive interactions to form a soliton in a nonlinear system. Our results will be applicable in general to the Anderson localization in nonlinear systems that have solitons.