Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

TL;DR

This paper introduces a unified method for analyzing the stability and instability of positive lattice solitons in multi-dimensional nonlinear media, distinguishing between amplitude and drift instabilities based on stability condition violations.

Contribution

It provides a novel unified framework for qualitative and quantitative analysis of soliton stability in various lattice configurations, including periodic and quasiperiodic structures.

Findings

Violation of the slope condition causes amplitude instability.

Violation of the spectral condition causes drift instability.

The approach predicts stability and instability strength quantitatively.

Abstract

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to an amplitude instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength.