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

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.

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Cited by in corpus (28)

• Solitons in nonlinear lattices
• Solitons in combined linear and nonlinear lattice potentials
• Stable two-dimensional solitons in nonlinear lattices
• Solitary wave in the Nonlinear Dirac Equation with arbitrary nonlinearity
• Two-dimensional discrete solitons in dipolar Bose-Einstein condensates
• Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions
• Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices
• Interface solitons in one-dimensional locally-coupled lattice systems
• Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
• Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity
• Localized standing waves in inhomogeneous Schrodinger equations
• Self-localized Solitons of a q-Deformed Quantum System
• Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
• Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions
• Stable structures with high topological charge in nonlinear photonic quasicrystals
• A refined empirical stability criterion for nonlinear Schroedinger solitons under spatiotemporal forcing
• Conjugate gradient method for finding fundamental solitary waves
• Reversible Self-Replication of Spatio-Temporal Kerr Cavity Patterns
• Surface solitons in trilete lattices
• Dynamics of temporal Kerr cavity solitons in the presence of rapid parameter inhomogeneities: from bichromatic driving to third-order dispersion
• Interface solitons in locally linked two-dimensional lattices
• Supersolid Gap Soliton in a Bose-Einstein Condensate and Optical Ring Cavity coupling system
• Positive and necklace solitary waves on bounded domains
• Stationary states of a nonlinear Schrödinger lattice with a harmonic trap
• Probing non-locality of interactions in a Bose-Einstein Condensate using solitons
• Band-edge solitons, Nonlinear Schrodinger / Gross-Pitaevskii Equations and Effective Media
• Splendeurs et misères de theory of laser beam propagation in nonlinear media
• Self-Localized Solitons of the Nonlinear Wave Blocking Problem