Dark Solitons in Discrete Lattices: Saturable versus Cubic Nonlinearities

Abstract

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them with those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both on-site and inter-site modes, are examined analytically and corroborated by numerical results. Furthermore, their dynamical evolution when they are found to be unstable is obtained through appropriately crafted numerical experiments.

arXiv comment15 pages, 5 figures

References in corpus (15)

• Discrete Breathers
• Bright gap solitons of atoms with repulsive interaction
• Observation of discrete vortex solitons in optically-induced photonic lattices
• Theory of Nonlinear Matter Waves in Optical Lattices
• Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
• Superfluid current disruption in a chain of weakly coupled Bose-Einstein Condensates
• Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review
• Asymmetric Landau-Zener tunneling in a periodic potential
• Discreteness-Induced Oscillatory Instabilities of Dark Solitons
• Defect modes in one-dimensional photonic lattices
• Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schrödinger Equation
• Radiationless Travelling Waves In Saturable Nonlinear Schrödinger Lattices
• Growth and decay of discrete nonlinear Schroedinger breathers interacting with internal modes or standing-wave phonons
• Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays
• Discrete soliton collisions in a waveguide array with saturable nonlinearity

Cited by in corpus (15)

• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices
• Localized gap soliton trains of Bose-Einstein condensates in an optical lattice
• Discrete solitons in electromechanical resonators
• Dark lattice solitons in one-dimensional waveguide arrays with defocusing saturable nonlinearities and alternating couplings
• Stability and instability for subsonic travelling waves of the Nonlinear Schrödinger Equation in dimension one
• Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
• Interlaced solitons and vortices in coupled DNLS lattices
• Nanoptera In Higher-Order Nonlinear Schrödinger Equations: Effects Of Discretization
• Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice
• Existence, Stability and Dynamics of Discrete Solitary Waves in a Binary Waveguide Array
• Soliton shape and mobility control in optical lattices
• Solitons in a parametrically driven damped discrete nonlinear Schrödinger equation
• Maxwell Fronts in the Discrete Nonlinear Schrödinger Equations with Competing Nonlinearities
• Stability of discrete dark solitons in nonlinear Schrodinger lattices