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

Y. Sivan, G. Fibich, B. Ilan, M. I. Weinstein

Research output: Contribution to journalArticlepeer-review

Abstract

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional 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 a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.

Original languageEnglish
Article number046602
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume78
Issue number4
DOIs
StatePublished - 2 Oct 2008

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