Drift instability and tunneling of lattice solitons

TL;DR

This paper derives an analytic formula for the lateral dynamics of lattice solitons in inhomogeneous media, revealing conditions for stability and tunneling behavior, with implications for understanding soliton motion over extended distances.

Contribution

It introduces a new analytic approach to describe soliton dynamics in inhomogeneous media, including stability analysis and tunneling bounds, surpassing traditional Peierls-Nabarro methods.

Findings

Solitons at lattice maxima can be mathematically unstable but physically stable.

An upper bound for the critical tunneling velocity is derived.

The formula remains valid over tens of diffraction lengths.

Abstract

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be ``mathematically unstable'' but ``physically stable''. We also derive an analytic upper bound for the critical velocity for tunneling, which is valid even when the standard Peierls-Nabarro potential approach fails.