Soliton Trapping in Disordered Lattice
Disordered Systems and Neural Networks
2015-01-20 v1
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.
Cite
@article{arxiv.1501.04231,
title = {Soliton Trapping in Disordered Lattice},
author = {Zhi-Yuan Sun and Shmuel Fishman and Avy Soffer},
journal= {arXiv preprint arXiv:1501.04231},
year = {2015}
}