Drift instability and tunneling of lattice solitons

Abstract

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be ``mathematically unstable'' but ``physically stable''. We also derive an analytic upper bound for the critical velocity for tunneling, which is valid even when the standard Peierls-Nabarro potential approach fails.

References in corpus (7)

• Bifurcations and stability of gap solitons in periodic potentials
• A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
• Soliton mobility in nonlocal optical lattices
• Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity
• Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials
• Temporal dynamics of tunneling. Hydrodynamic approach
• Analytic theory of narrow lattice solitons

Cited by in corpus (6)

• Bright solitons from defocusing nonlinearities
• Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
• Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity
• Reflection, Transmission and Trapping Dynamics of Lattice Solitons at Interfaces
• Solitons supported by spatially inhomogeneous nonlinear losses
• Positive and necklace solitary waves on bounded domains