Motion of discrete solitons assisted by nonlinearity management

Abstract

We demonstrate that periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schrödinger (DNLS) equation can strongly facilitate creation of traveling solitons in the lattice. We predict this possibility in an analytical form, and test it in direct simulations. Systematic simulations reveal several generic dynamical regimes, depending on the amplitude and frequency of the time modulation, and on initial thrust which sets the soliton in motion. These regimes include irregular motion, regular motion of a decaying soliton, and regular motion of a stable one. The motion may occur in both the straight and reverse directions, relative to the initial thrust. In the case of stable motion, extremely long simulations in a lattice with periodic boundary conditions demonstrate that the soliton keeps moving as long as we can monitor without any visible loss. Velocities of moving stable solitons are in good agreement with the analytical prediction, which is based on requiring a resonance between the ac drive and motion of the soliton through the periodic potential. All the generic dynamical regimes are mapped in the model's parameter space. Collisions between moving stable solitons are briefly investigated too, with a conclusion that two different outcomes are possible: elastic bounce, or bounce with mass transfer from one soliton to the other. The model can be realized experimentally in a Bose-Einstein condensate trapped in a deep optical lattice.

References in corpus (9)

• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Bright gap solitons of atoms with repulsive interaction
• Nonlinear excitations in arrays of Bose-Einstein condensates
• Nonlinear Self-Trapping of Matter Waves in Periodic Potentials
• Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
• Nonlinear Tight-Binding Approximation for Bose-Einstein Condensates in a Lattice
• Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields
• Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management
• Observation of progressive motion of ac-driven solitons

Cited by in corpus (9)

• Moving solitons in the discrete nonlinear Schrödinger equation
• Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices
• Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation
• Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity
• Quantum switches and quantum memories for matter-wave lattice solitons
• Parametric resonance of a Bose-Einstein condensate in a ring trap with periodically driven interactions
• Accurate control of a Bose-Einstein condensate by managing the atomic interaction
• Application of the Feshbach-resonance management to a tightly confined Bose-Einstein condensate
• Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices