Solitary Waves in a Discrete Nonlinear Dirac equation

Abstract

In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-continuum limit of vanishing coupling). Numerous unexpected features are identified including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site, respectively, excitations of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states are identified, as well as instabilities that appear to be persistent over the coupling strength $\epsilon$, for a subcritical value of the propagation constant $\Lambda$. Variations of the propagation constant, coupling parameter and nonlinearity exponent are all examined in terms of their existence and stability implications and long dynamical simulations are used to unravel the evolutionary phenomenology of the system (when unstable).

References in corpus (31)

• A spin-orbit coupled Bose-Einstein condensate
• Artificial gauge potentials for neutral atoms
• Synthetic magnetic fields for ultracold neutral atoms
• Collective Dipole Oscillation of a Spin-Orbit Coupled Bose-Einstein Condensate
• Observation of Zitterbewegung in a spin-orbit coupled Bose-Einstein condensate
• Matter-wave bright solitons in spin-orbit coupled Bose-Einstein condensates
• The creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space
• Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
• Bright solitons in spin-orbit-coupled Bose-Einstein condensates
• Gap solitons in the spin-orbit coupled Bose-Einstein condensates
• Stable Skyrmions in SU(2) Gauged Bose-Einstein Condensates
• Spin-Orbit Coupled Bose-Einstein Condensate under Rotation
• Direct observation of zitterbewegung in a Bose-Einstein condensate
• Half-quantum vortex state in a spin-orbit coupled Bose-Einstein condensate
• Vortices in spin-orbit-coupled Bose-Einstein condensates
• Discreteness-Induced Oscillatory Instabilities of Dark Solitons
• Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schrödinger Equation
• Radiationless Travelling Waves In Saturable Nonlinear Schrödinger Lattices
• Chiral confinement in quasirelativistic Bose-Einstein condensates
• Breathers and surface modes in oscillator chains with Hertzian interactions
• Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity
• Soliton Magnetization Dynamics in Spin-Orbit Coupled Bose-Einstein Condensates
• Numerical methods for nonlinear Dirac equation
• Matter-wave dark solitons and their excitation spectra in spin-orbit coupled Bose-Einstein condensates
• Solitary wave in the Nonlinear Dirac Equation with arbitrary nonlinearity
• Orbital stability of Dirac solitons
• Line of Dirac monopoles embedded in a Bose-Einstein condensate
• On spectral stability of solitary waves of nonlinear Dirac equation on a line
• Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity
• Nonlinear Dirac equation solitary waves in external fields
• Discrete gap solitons in a diffraction-managed waveguide array

Cited by in corpus (9)

• Stability of solitary waves and vortices in a 2D nonlinear Dirac model
• Dynamics of Dirac solitons in networks
• The mass of simple and higher-order networks
• Solitary waves in the Nonlinear Dirac Equation
• Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
• Integrable semi-discretization of the massive Thirring system in laboratory coordinates
• A PT-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling
• Enhanced mobility of discrete solitons in anisotropic two-dimensional waveguide arrays with modulated separations
• Stability of parametrically driven, damped nonlinear Dirac solitons