Soliton Mobility in Disordered Lattice

TL;DR

This paper studies how disorder affects soliton movement in nonlinear lattices, introducing an effective potential to analyze dynamics and proposing methods to enhance soliton transport despite randomness.

Contribution

It introduces a generalized effective potential for disordered nonlinear lattices and demonstrates its usefulness in analyzing and improving soliton mobility.

Findings

Disorder influences soliton mobility via an effective potential.

Soliton size impacts its ability to move in disordered lattices.

Specific disorder realizations and soliton pairs can enhance transport.

Abstract

We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schr\"{o}dinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from deviation from integrability, resulting of randomness for the AL model, and of both randomness and lattice discreteness for the NLS lattice. Statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size. The usefulness of this effective potential in studying soliton dynamics is demonstrated numerically. Further we propose two ways the soliton transport in presence of disorder can be enhanced: one is to use specific realizations of randomness, and the other one is to consider a specific soliton pair.