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

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

2008-06-24

arxiv.org/abs/0806.3838v2

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1103/PhysRevE.78.046602

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.

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