Modulational instability and discrete breathers in the discrete cubic-quintic nonlinear Schrödinger equation

We investigate the properties of modulational instability and discrete breathers in the cubic-quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. Using the Page approach [J.B. Page, Phys. Rev. B 41 (1990) 7835], we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The application to the existence of localized modes in the Bose-Einstein condensate (BEC) with three-body interactions in an optical lattice is discussed. The numerical simulations agree with the analytical predictions.     

Modulational instability,quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field

The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.     

Intrinsic Localized Spin Wave Modes and Modulational Instability in a Two-Dimensional Heisenberg Ferromagnet

An analytical study on the properties of intrinsic localized modes and modulational instability in a quantum two-dimensional ferromagnet with single-ion uniaxial anisotropy is completed in the semiclassical limit. By making use of the semidiscrete multiple-scale method, we obtain a line localized solution and a radially symmetric localized solution, and analyze their existence conditions. Taking into account that the existence of bright localized solutions is closely linked to the modulational instability of plane waves, we analytically study the discrete modulational instability of plane spin waves. The result of the modulational instability analysis show that the uniaxial anisotropy plays a key role in the appearance of our intrinsic localized spin wave modes.     

Excitation of Convective Cells by Nonlinear Interaction of Interchange Mode

Convective Cell formation due to nonlinear interaction of interchange mode is studied using multiple time and space scales. Basic interchange mode equation is modified to obtain nonlinear localized structure with modulational perturbation in the drift direction and periodic boundary condition for the perturbation in the direction of the density gradient. To study modulational instability we have deduced nonlinear evolution equation for the first order perturbation from third order secularity elimination condition. Modulational instability, which is responsible for localized structure, is studied in two limits of the dispersion relation.     

Intrinsic Localized Modes in Quantum Ferromagnetic XXZ Chains in an Oblique Magnetic Field

A semiclassical study of intrinsic localized spin-wave modes in a one-dimensional quantum ferromagnetic XXZ chain in an oblique magnetic field is presented in this paper. We quantize the model Hamiltonian by introducing the Dyson-Maleev transformation, and adopt the coherent state representation as the basic representation of the system. By means of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude can be reduced to the standard nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, when θ < θ _c a bright intrinsic localized spin-wave mode appears below the bottom of the magnon frequency band and when θ > θ _c a dark intrinsic localized spin-wave resonance mode can occur above the bottom of the magnon frequency band. In other words, the switch between the bright and dark intrinsic localized spin-wave modes can be controlled via varying the angle of the magnetic field. This result has potential applications in quantum information storage. In addition, we find that, at the boundary of the Brillouin zone, the system can only produce a dark intrinsic localized spin-wave mode, whose eigenfrequency is above the upper of the magnon frequency band.     

Brillouin-zone mapping of the spin waves in a ferromagnetic bilayer system

The eigenproblems of spin waves in a heterogeneous ferromagnetic bilayer system with periodic boundary conditions are solved using the interface-rescaling approach. Brillouin zone mapping and the eigenmodes of the system are investigated. We find three types of spin waves may exist in the system: the bulk mode, the interface mode, and the perfect confined mode. The fine structure of the energy band in the heterogeneous bilayer system is first given for the whole two-dimensional Brillouin zone. Conditions for the existence of the interface mode are discussed. Finally, we analyze the resonant-confined spin waves in bulk modes and their oscillating behavior.     

Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j=j₀.     

Instability and evolution of nonlinearly interacting water waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schr?dinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.     

玻色凝聚的原子自旋链中的非线性自旋波

研究了囚禁在光晶格中的旋量玻色-爱因斯坦凝聚体(BEC)形成的原子自旋链中的相干非线性自旋波的激发与调制不稳定性.通过解析分析，得到了调制不稳定性的一般判据以及其对原子自旋的长程耦合的依赖关系.在蓝失谐和红失谐光晶格的情况下，分别具体分析了长程非线性自旋耦合，包括光诱导的和静磁诱导的偶极-偶极相互作用对相干自旋波调制不稳定性的影响.     

Optical vortex solitons in parametric wave mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.     

On diffraction and dispersion effect on three wave interaction

The effect of diffraction and dispersion on three wave coupling is investigated. The instability leading to space modulation of packets is obtained. This instability and its nonlinear stage is similar to modulational instability of quasimonochromatic waves. The localized structures (solitons and waveguide) can be a result of the instability. We demonstrate that one-dimensional and two-dimensional such structures are unstable. The existence of stable three-dimensional solitons is shown.     

具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模(英文)

基于Hartree-Fock方法和多标度方法,我们考察了具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模,量子磁振子的波函数由量子包络孤子来描述.在布里渊区边界,量子包络孤子变成了量子内禀局域模,它的量子本征频率在简谐波带的顶部上方,量子磁振子主要集中在中心位置j=j0的附近.     

Modulational Instability and Energy Localization in a Chain of Interacting Frenkel Excitons

The modulational instability in one-dimensional molecule chain of interacting Frenkel excitons is investigated. The formation of localized modes via modulational instability is predicted and the previous numerical and analytical results are explained. The Peierls-Nabarro (PN) potential barrier for the localized modes is also discussed.     

Quantum Solitary Wave Solutions in a Ferromagnetic Chain with Nearest- and Next-Nearest-Neighbor Interaction

The quantum solitary wave solutions in a one-dimensional ferromagnetic chain is investigated by using the Hartree-Fock approach and the multiple-scale method. It is shown that quantum solitary wave solutions can exist in a ferromagnetic system with nearest- and next-nearest-neighbor exchange interaction, and at the certain value of the first Brillouin zone, the solitary wave solution of the Hartree wave function becomes the intrinsic localized mode.     

TWO-DIMENSIONAL LOCALIZED VIBRATIONAL MODES AROUND A POLARON WITH THE NEXT-NEAREST-NEIGHBOR HOPPING INTERACTIONS

We have calculated the vibrational modes around a polaron to test the effects of the next-nearest-neighbor hopping interactions on the localized medes within a framework of the two-dimensional mode. The results show that: (1) For a negative polaron, eleven localized modes have been found, compared with ten modes obtained on a previous work without non-nearest neighbor hopping. (2) For a positive polaron, two additional localized modes occur. (3) The localization of localized modes are strengthened and their frequencies move after turning on the next-nearest-neighbor hopping interactions.     

The modulation instability revisited

The modulational instability (or “Benjamin-Feir instability”) has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency downshifting affects the evolution in ways that are still poorly understood.     

Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays

We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the formation of regular periodic or quasiperiodic modulations of the polarization. We reveal that such nonlinear nanoparticle arrays can support long-lived standing and moving oscillating nonlinear localized modes--plasmon oscillons.     

Saturation of backward stimulated scattering of a laser beam in the kinetic regime

Stimulated Raman (SRS) and Brillouin scattering (SBS) are examined in the kinetic regime using particle-in-cell simulations. Wave front bowing of electron-plasma waves (ion-acoustic waves) from trapped particle nonlinear frequency shift is observed in the SRS (SBS) regime for the first time. Self-focusing from trapped particle modulational instability (TPMI) is shown to occur in 2D and 3D SRS simulations. The key physics of SRS saturation is identified as a combination of wave front bowing, TPMI, and self-focusing: Bowing marks the beginning of SRS saturation and self-focusing terminates SRS. Ion-acoustic wave bowing also contributes to SBS saturation. Velocity diffusion by transverse modes and rapid loss of hot electrons in regions of small transverse extent formed from self-focusing dissipate wave energy and increase Landau damping, despite trapping that reduces Landau damping initially.     

Solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain

By use of the Hartree approximation and the method of multiple scales, we investigate quantum solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain. It is shown that there exist solitons of two different quantum frequency bands: i.e., magnetic optical solitons and acoustic solitons. At the boundary of the Brillouin zone, these solitons become quantum intrinsic localized modes: their quantum eigenfrequencies are below the bottom of the harmonic optical frequency band and above the top of the harmonic acoustic frequency band.     

The effect of quasinesting and a magnon mode on the antiferromagnetic vector for the optical conductivity of a doped two-dimensional antiferromagnet

The optical spectrum of the normal state of a doped two-dimensional antiferromagnet is analyzed in a Kondo lattice model with regard to the complex structure of a spin polaron. The optical properties are determined by sharply anisotropic scattering of spin-polaron excitations by antiferromagnetic fluctuations of a system of localized spins. It is shown that the relaxation of carriers in the infrared range is mainly attributed to the strong coupling between these carriers and the mode of low-frequency spin excitations with the quasimomentum close to the antiferromagnetic vector Q=(π,π). The latter coupling is associated with the fact that the regions of the Fermi surface of the lower polaron band are close to the boundary of the antiferromagnetic Brillouin zone. The calculated optical characteristics are in qualitative agreement with experimental data for the normal state of high-temperature superconductors (HTSCs).