Soliton Trapping in Disordered Lattice

TL;DR

This paper investigates how random potentials affect soliton dynamics in the Ablowitz-Ladik model, revealing regimes of stable and particle-like behavior, and deriving an effective potential that predicts soliton motion changes.

Contribution

It introduces an effective potential framework for understanding soliton behavior in disordered lattices, extending the analysis of stability and dynamics under randomness.

Findings

Random potential destroys soliton stability in the integrable model.

Identifies regimes of constant and varying mass particle-like dynamics.

Derives a scaling relation between soliton direction change time and potential strength.

Abstract

Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In absence of the random potential it is an integrable model and the solitons are stable. As a result of the random potential this stability is destroyed. In some regime, for short times particle-like dynamics with constant mass is found. There is another regime, where particle-like dynamics with varying mass takes place. In particular an effective potential is found. It predicts correctly changes in the direction of motion of the soliton. This potential is a scaling function of time and strength of the potential, leading to a relation between the first time when the soliton changes direction and the strength of the random potential.