Collapse arrest and soliton stabilization in nonlocal nonlinear media
arXiv:nlin/0201036 · doi:10.1103/PhysRevE.66.046619
Abstract
We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.
4 pages with 3 figures
References in corpus (9)
- Theory of Bose-Einstein condensation in trapped gases
- Black Holes
- Modulational instability in nonlocal nonlinear Kerr media
- Bose-Einstein condensation with magnetic dipole-dipole forces
- Solitons in nonlocal nonlinear media: exact results
- Structure and stability of bosonic clouds: alkali atoms with negative scattering length
- Stability of Bose condensed atomic Li-7
- Nonlocal interactions prevent collapse in negative scattering length Bose-Einstein gases
- Correlation induced collapse of many-body systems with zero-range potentials
Cited by in corpus (99)
- Fractional Schrodinger equation
- The physics of dipolar bosonic quantum gases
- Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
- Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media
- Two-dimensional bright solitons in dipolar Bose-Einstein condensates
- Observation of attraction between dark solitons
- Two-dimensional multi-pole solitons in nonlocal nonlinear media
- Generic features of modulational instability in nonlocal Kerr media
- Stability of two-dimensional spatial solitons in nonlocal nonlinear media
- Stable rotating dipole solitons in nonlocal optical media
- Quadratic solitons as nonlocal solitons
- A new nonlocal nonlinear Schroedinger equation and its soliton solutions
- Optical spatial solitons in soft-matter: mode coupling theory approach
- Soliton mobility in nonlocal optical lattices
- Analytical theory for dark soliton interaction in nonlocal nonlinear materials with arbitrary degree of nonlocality
- Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media
- Phonon instability in two-dimensional dipolar Bose-Einstein Condensates
- Linearons: highly non-instantaneous solitons in liquid-core photonic crystal fibers
- Stability of dark solitons in three dimensional dipolar Bose-Einstein condensates
- Nonlocal incoherent solitons
- Perturbative analysis of generally nonlocal spatial optical solitons
- Strong interaction between plants induces circular barren patches: fairy circles
- Controllable Raman-like nonlinearities from non-stationary cascaded quadratic processes
- Spatial solitons and modulational instability in the presence of large birefringence: the case of highly non-local liquid crystal
- Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
- Scattering of two-dimensional solitons in dipolar Bose-Einstein condensates
- On localized vegetation patterns, fairy circles and localized patches in arid landscapes
- Analytical theory of dark nonlocal solitons
- Super-mode spatial optical solitons in liquid crystals with competing nonlinearities
- Creating two-dimensional bright solitons in dipolar Bose-Einstein condensates
- Stabilization of vector soliton complexes in nonlocal nonlinear media
- Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality
- Observation of migrating transverse Anderson localizations of light in nonlocal media
- Two dimensional bright solitons in dipolar Bose-Einstein condensates with tilted dipoles
- Robust ultrashort light bullets in strongly twisted waveguide arrays
- Light bullets in Bessel optical lattices with spatially modulated nonlinearity
- Optomechanical self-channelling of light in a suspended planar dual-nanoweb waveguide
- Spatiotemporal control of laser intensity through cross-phase modulation
- Spatial solitons in thermo-optical media from the nonlinear Schrodinger-Poisson equation and dark matter analogues
- Light bullets in optical tandems
- Nonlinear continuous-wave optical propagation in nematic liquid crystals: interplay between reorientational and thermal effects
- Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices
- Formation of localized structures in bistable systems through nonlocal spatial coupling I: General framework
- Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential
- Rogue waves in nonlocal media
- Azimuthons in weakly nonlinear waveguides of different symmetries
- Symmetry breaking in dipolar matter-wave solitons in dual-core couplers
- Anderson Localization in Nonlocal Nonlinear Media
- Complex light: Dynamic phase transitions of a light beam in a nonlinear non-local disordered medium
- Lattice solitons with quadrupolar intersite interactions
- Rotating soliton solutions in nonlocal nonlinear media
- The Relation Between Optical beams Propagation in Free Space and in Strongly Nonlocal Nonlinear Media
- Bose-Einstein condensation of photons with nonlocal nonlinearity in a dye-doped graded-index microcavity
- Rotating three-dimensional solitons in Bose Einstein condensates with gravity-like attractive nonlocal interaction
- Gap solitons under competing local and nonlocal nonlinearities
- Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation
- Tracking azimuthons in nonlocal nonlinear media
- Robust three-dimensional high-order solitons and breathers in driven dissipative systems: a Kerr cavity realization
- Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium
- Collapse suppression and stabilization of dipole solitons in two-dimensional media with anisotropic semi-local nonlinearity
- Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics
- Optical Spatial Shock Waves in Nonlocal Nonlinear Media
- Quantum gravity simulation by non-paraxial nonlinear optics
- Stability of solitary waves in random nonlocal nonlinear media
- Modulational instability in nonlocal Kerr-type media with random parameters
- Arrays of stochastic oscillators: Nonlocal coupling, clustering, and wave formation
- Elastic-like Collision of Gap Solitons in Bragg Gap Regions within Nonlocal Nonlinear Photonic Crystals
- Light bullets in Su-Schrieffer-Heeger photonic topological insulators
- Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides
- Modulation instability and solitons in two-color nematic crystals
- Effective attraction between oscillating electrons in a plasmoid via acoustic waves exchange
- Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction
- Self-bound droplets of light with orbital angular momentum
- High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices
- Solitary modes in nonlocal media with inhomogeneous self-repulsive nonlinearity
- Large phase shift of (1+1)-dimensional nonlocal spatial solitons in lead glass
- Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential
- Dynamics of optomechanical spatial solitons in dual-nanoweb structures
- Accessing and Manipulating Dispersive Shock Waves in a Nonlinear and Nonlocal Rydberg Medium
- Semiclassical states for Choquard type equations with critical growth: critical frequency case
- Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
- Effects of Long-Range Nonlinear Interactions in Double-Well Potentials
- Soliton solutions of the non-linear Schroedinger equation with nonlocal Coulomb and Yukawa-interactions
- Gap solitons in optical lattices embedded into nonlocal media
- Variational approach to multidimensional solitons in highly nonlocal nonlinear media
- Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media
- Existence and stability of standing waves for coupled nonlinear Hartree type equations
- Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and symmetry
- Transverse instability and dynamics of nonlocal bright solitons
- Solitary Wave Formation under the Interplay between Spatial Inhomogeneity and Nonlocality
- Mobility of nonlocal solitons in fading optical lattices
- Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation
- New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and Matter
- Pitch-controlled reorientational nonlinearity in chiral nematic liquid crystals: a reduced-order model for self-focusing and soliton formation
- Temporal dynamics of light-written waveguides in unbiased liquid crystals
- Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
- Observation of Optical Solitons and Abnormal Modulation Instability in Liquid Crystals with Negative Dielectric Anisotropy
- Quasi-two-dimensional soliton in a self-repulsive spin-orbit-coupled dipolar binary condensate
- Shortcuts to adiabaticity for rapid soliton compression in nonlocal media