Modulational instability in nonlocal nonlinear Kerr media
arXiv:nlin/0103003 · doi:10.1103/PhysRevE.64.016612
Abstract
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.
8 pages, submitted to Phys. Rev. E
Cited by in corpus (68)
- The physics of dipolar bosonic quantum gases
- Collapse arrest and soliton stabilization in nonlocal nonlinear media
- Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media
- Two-dimensional bright solitons in dipolar Bose-Einstein condensates
- 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
- Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media
- Walk-off-induced modulation instability, temporal pattern formation, and frequency comb generation in cavity-enhanced second-harmonic generation
- Solitons in quasi one-dimensional Bose-Einstein condensates with competing dipolar and local interactions
- Multipole vector solitons in nonlocal nonlinear media
- Soliton mobility in nonlocal optical lattices
- 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
- Ring dark and anti-dark solitons in nonlocal media
- Spatial solitons and modulational instability in the presence of large birefringence: the case of highly non-local liquid crystal
- Scattering of two-dimensional solitons in dipolar Bose-Einstein condensates
- On localized vegetation patterns, fairy circles and localized patches in arid landscapes
- Bright solitons in a 2D spin-orbit-coupled dipolar Bose-Einstein condensate
- New features of modulational instability of partially coherent light; importance of the incoherence spectrum
- Stabilization of vector soliton complexes in nonlocal nonlinear media
- Solitons in Tonks-Girardeau gas with dipolar interactions
- Modulation instability in high-order coupled nonlinear Schrödinger equations with saturable nonlinearities
- Relation between surface solitons and bulk solitons in nonlocal nonlinear media
- 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
- Formation of localized structures in bistable systems through nonlocal spatial coupling II: The nonlocal Ginzburg Landau Equation
- Rogue waves in nonlocal media
- Black and gray spatial optical solitons with Kerr type nonlocal nonlinearity
- Localized structures in dispersive and doubly resonant optical parametric oscillators
- Azimuthal Modulational Instability of Vortices in the Nonlinear Schrödinger Equation
- Symmetry breaking in dipolar matter-wave solitons in dual-core couplers
- Rotating soliton solutions in nonlocal nonlinear media
- Spatially incoherent modulational instability in a non local medium
- Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices
- Modulational instability in nonlocal Kerr media with sine-oscillatory response
- Complex variable function Gaussian beam in strongly nonlocal nonlinear media
- Singular instability of exact stationary solutions of the nonlocal Gross-Pitaevskii equation
- Nonlocality and fluctuations near the optical analog of a sonic horizon
- Elastic-like Collision of Gap Solitons in Bragg Gap Regions within Nonlocal Nonlinear Photonic Crystals
- Modulational instability in nonlocal Kerr-type media with random parameters
- Arrays of stochastic oscillators: Nonlocal coupling, clustering, and wave formation
- Self-organized structures of two-component laser fields and their active controls in a cold Rydberg atomic gas
- Modulation instability and solitons in two-color nematic crystals
- Structural Phase Transitions of Optical Patterns in Atomic Gases with Microwave Controlled Rydberg Interactions
- High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices
- Programmable photonic time circuits for highly scalable universal unitaries
- Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction
- Ginzburg-Landau equation for dynamical four-wave mixing in gain nonlinear media with relaxation
- Accessing and Manipulating Dispersive Shock Waves in a Nonlinear and Nonlocal Rydberg Medium
- A generalized nonlinear Schrödinger equation as model for turbulence, collapse, and inverse cascade
- Nonlocal nonlinear response of thermal Rydberg atoms and modulational instability in absorptive nonlinear media
- Gap solitons in optical lattices embedded into nonlocal media
- Effects of Long-Range Nonlinear Interactions in Double-Well Potentials
- Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models
- Probing non-locality of interactions in a Bose-Einstein Condensate using solitons
- Resonance in modulation instability from non-instantaneous nonlinearities
- (2+1)D surface solitons at the interface between a linear medium and a nonlocal nonlinear medium
- Stability of the NLS equation with viscosity effect
- Propagation-Distance Limit for a Classical Nonlocal Optical System
- Pitch-controlled reorientational nonlinearity in chiral nematic liquid crystals: a reduced-order model for self-focusing and soliton formation
- Chirped periodic and localized waves in a weakly nonlocal media with cubic-quintic nonlinearity
- Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
- Shortcuts to adiabaticity for rapid soliton compression in nonlocal media
- Stable single light bullets and vortices and their active control in cold Rydberg gases