Two-component coupled photovoltaic soliton pair in two-photon photorefractive materials under open circuit conditions

The existence and nonlinear dynamics of two-component incoherently coupled composite solitons in two-photon photorefractive materials under open circuit conditions have been investigated. In the steady-state regime, these incoherently coupled solitons can propagate in bright–dark, bright–bright and dark–dark configurations. These photovoltaic soliton families can be established provided that the carrier beams share the same polarization and wavelength. The influence of the gating beam on the dynamics of stable solitons is discussed. Numerical simulations show that these solitons are stable for small perturbation on amplitude.     

Dynamically compressed bright and dark solitons in highly anisotropic Bose-Einstein condensates

Bright and dark matter wave solitons are constructed analytically in a three-dimensional (3D) highly anisotropic Bose-Einstein condensate (BEC) with a time-dependent parabolic potential, and numerical simulations are performed to confirm the existence and dynamics of such analytical solutions. Different classes of bright and dark solitons are discovered among the solutions of the generalized anisotropic (3+1)D Gross-Pitaevskii equation. Our results demonstrate that the bright and dark solitary waves can be manipulated and controlled by changing the scattering length, which can be used to compress the second-order bright and dark solitons of BECs into desired peak density.     

Holographic solitons in centrosymmetric photorefractive crystals

The conditions necessary for obtaining holographic solitons in centrosymmetric photorefractive crystals are discussed. When both the intensity modulation of the two interacting waves and the angle between the vector of each beam and the longitudinal axis are small, centrosymmetric photorefractive crystals with a positive (or negative ) effective quadratic electro-optic coefficient are able to support bright (or dark) holographic solitons. The intensity width at half maximum of bright and dark solitons is inversely proportional to the external bias field. The holographic solitons can also exit in dissipative centrosymmetric photorefractive crystals when the applied external bias field is large enough.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Magnetized vector solitons in a spin-orbit coupled spin-1 Bose-Einstein condensate with Zeeman coupling

The property of matter-wave vector solitons in a spin-1 Bose-Einstein condensate with spin-orbit and Zeeman couplings is investigated by multiscale perturbation method. The excitation spectrum and the corresponding state vectors of the system are obtained analytically, and they can be adjusted by the parameters of the system. The bright and dark vector solitons are formulated by reducing the three-component coupled Gross-Pitaeviskii equations to a standard nonlinear Schrödinger equation, which has the solutions of the bright and dark solitons with positive or negative mass depending on the product of the effective dispersive and nonlinear coefficients. The moving vector solitons are demonstrated by adjusting specific momentum near the energy minimum. Finally, the magnetized features of the vector solitons are discussed by the spin polarization of the system.     

Interference properties of two-component matter wave solitons

Wave properties of solitons in a two-component Bose-Einstein condensate are investigated in detail.We demonstrate that dark solitons in one of components admit interference and tunneling behavior,in sharp contrast to the scalar dark solitons and vector dark solitons.Analytic analyses of interference properties show that spatial interference patterns are determined by the relative velocity of solitons,while temporal interference patterns depend on the velocities and widths of two solitons,differing from the interference properties of scalar bright solitons.Especially,for an attractive interactions system,we show that interference effects between the two dark solitons can induce some short-time density humps(whose densities are higher than background density).Moreover,the maximum hump value is remarkably sensitive to the variation of the solitons' parameters.For a repulsive interactions system,the temporal-spatial interference periods of dark-bright solitons have lower limits.Numerical simulation results suggest that interference patterns for the dark-bright solitons are more robust against noises than bright-dark solitons.These explicit interference properties can be used to measure the velocities and widths of solitons.It is expected that these interference behaviors can be observed experimentally and can be used to design matter wave soliton interferometer in vector systems.     

Do solitonlike self-similar waves exist in nonlinear optical media?

We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.     

Soliton interaction in the coupled mixed derivative nonlinear Schrödinger equations

The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schrödinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.     

Frequency characteristics of the dark and bright surface solitons at a nonlinear metamaterial interface

We investigate the generation and properties of dark and bright surface waves at the interface of a conventional medium and a metamaterial. It is shown that the stable dark and bright surface solitons can coexist even when the nonlinear Kerr coefficients of the two media are negative, completely different from those at the interface between two conventional media. Most importantly, both the dark and bright surface solitons exist only within a certain range of the effective refractive index of the metamaterial, greatly depending on the frequency of the electromagnetic wave propagating in it. Therefore, the generation conditions for surface solitons, and the properties of the generated surface solitons such as the peak positions and the intensity of the dark and bright surface solitons, can be controlled by adjusting the structure parameters of the metamaterial and/or the frequency of the electromagnetic wave.     

Collision of bright vector solitons in two-component Bose-Einstein condensates

We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons.     

暗-暗与亮-暗光伏孤子相互作用

用数值方法分析了平行传播异色光伏暗孤子之间及亮-暗孤子之间的相互作用.结果表明，光伏暗孤子共轴传播能在有限的距离内保持准孤子形态，靠近传播时存在着相互吸引的作用 ，而相距较远传播时表现为一孤子暗区使另一孤子的缓变光场部分发生局部会聚作用.光伏暗孤子与亮孤子的相互作用随距离的不同可使亮孤子光强分布变尖锐或变平缓，以及使亮孤子发生能量转移.从两束信号光共同引起折射率波导这一物理机理对光伏孤子这些相互作用给出定性物理解释. 关键词： 光伏空间孤子 暗孤子 亮孤子 相互作用     

Bright and dark solitons for a variable-coefficient $$$$ dimensional Heisenberg ferromagnetic spin chain equation

Under investigation in this paper is a variable-coefficient \((2+1)\) dimensional Heisenberg ferromagnetic spin chain equation. Bilinear forms for the bright and dark soliton solutions are respectively obtained. Bright and dark solitons are obtained via the Hirota bilinear method. Features of the bright and dark solitons are discussed. Interaction properties of the bright and dark solitons are discussed via the asymptotic analysis, and stability of the bright and dark solitons is studied via the numerical calculation: (1) Amplitudes of the bright and dark solitons are not related to the coefficient \(\delta _{4}(t)\), while the soliton velocities are related to \(\delta _{4}(t)\). (2) Interactions between the bright two solitons are shown to be elastic, while interactions between the dark two solitons could be elastic or inelastic, which is determined by the values of \(\rho \). (3) Numerical calculation indicates that the bright solitons could not resist the disturbance of small perturbations, while the dark solitons could resist the disturbance of small perturbations.     

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.     

Matter-Wave Solitons in Two-Dimensional Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap

We present three families of one-soliton solutions for (2+1)-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.     

飞秒暗孤子间相互作用的数值研究

通过数值模拟对飞秒暗孤子间的相互作用进行了研究，并且同飞秒亮孤子和皮秒暗孤子分别进行了比较，结果表明：同飞秒亮孤子相比，飞秒暗孤子间的相互作用比较小，前者表现为相互吸引、碰撞、合二为一，然后相互排斥，不具有周期性；而后者从一开始就相互排斥，且这种排斥作用较亮孤子来说相当微弱，同样也不具有周期性。此外，数值模拟的结果还表明，飞秒暗孤子间的相互作用同皮秒尺度下暗孤子间的相互作用基本一致，并且通过计算表明，飞秒暗孤子间的相互作用在一定范围内仍可利用皮秒尺度下暗孤子间相互作用的经验公式。但是，数值模拟结果显示，两孤子的初始间距越小，由经验公式计算结果所带来的误差就越大。     

Vectorial Kerr-cavity solitons

It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CS's). A parametrically driven Ginzburg-Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CS's is numerically investigated.     

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.     

Incoherently coupled two component screening photovoltaic solitons in two-photon photorefractive materials under the action of external field

The existence of incoherently coupled two-component steady state photovoltaic solitons in biased two-photon photorefractive materials due to two-photon photorefractive effect has been investigated. In the steady state regime, these incoherently coupled solitons can propagate in bright–bright, dark–dark and bright–dark configurations. The most important finding is that, with the application of electric field, it is possible to generate solitons and control them in those media where soliton formation was hitherto prohibited. Dynamic evolution of these solitons has been examined using numerical simulations, which show that these solitons are stable.     

Effects of Periodically Inhomogeneous Birefringence on Dark-Bright Vector Soliton Propagation and Interaction

The effects of periodically inhomogeneous birefringence on dark-bright vector soliton propagation and interaction are investigated by the numerical method. The birefringence leads to the submergence of the dark soliton and the disintegration of the bright soliton, and enhances the interaction between the neighbouring solitons. The system performance is determined by the bright soliton because the dark soliton has robust features. Finally, the avoidance and the effective control are introduced, and the controlling mechanism is demonstrated.