2008/06/30 by Yonatan Sivan, Y. Sivan, G. Fibich +5 · 1 citation
Physics and Astronomy · #Advanced Fiber Laser Technologies #Classical mechanics #Computer science #Condensed matter physics #Instability #Lattice (music) #Mechanics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Qualitative analysis #Qualitative research #Quantum mechanics #Quasiperiodic function #Soliton #Spectral analysis #Spectroscopy #Stability (learning theory) #Statistical physics #nlin.PS
paper · pdf · doi:10.1103/physreve.78.046602
arxiv created 2008/09/07 · openalex publication_date 2008/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.