Effect of a localized impurity on soliton dynamics in the Bose-Einstein condensates

By using a multiple-scale method,we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates.It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity,while at the position of the localized impurity the soliton can be quasitrapped by the impurity.Additionally,we find that the strength of the localized impurity has an important effect on the dark soliton dynamics.With increasing strength of the localized impurity,the amplitude of the dark soliton becomes bigger,while its width is narrower,and the soliton propagates slower.     

Dark Soliton of a Growing Bose--Einstein Condensate in an External Trap

The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.     

Trapping a dark soliton pulse within a nano ring resonator

We propose the interesting results that a dark soliton pulse can be localized within a nonlinear nano-waveguide. The system consists of nonlinear micro and nano ring resonators, whereas the dark soliton can be input into the system and trapped within the nano-waveguide. A dark soliton pulse is input into a ring resonator and chopped to be the smaller pulses. The required pulse is filtered and amplified, which can be controlled and localized within the nano-waveguide. The localized bright soliton is also reviewed and discussed.     

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose--Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.     

Vector kink-dark complex solitons in a three-component Bose–Einstein condensate

We investigate kink-dark complex solitons(KDCSs) in a three-component Bose–Einstein condensate(BEC) with repulsive interactions and pair-transition(PT) effects. Soliton profiles critically depend on the phase differences between dark solitons excitation elements. We report a type of kink-dark soliton profile which shows a droplet-bubble-droplet with a density dip, in sharp contrast to previously studied bubble-droplets. The interaction between two KDCSs is further investigated. It demonstrates some striking particle transition behaviours during their collision processes, while soliton profiles survive after the collision. Additionally, we exhibit the state transition dynamics between a kink soliton and a dark soliton. These results suggest that PT effects can induce more abundant complex solitons dynamics in multi-component BEC.     

Interaction of a dark soliton with a localized impurity

The interaction of a dark soliton governed by the nonlinear Schrödinger equation with a localized impurity is studied by means of a modified adiabatic approximation and direct numerical simulations. The prominent role of the rapidly varying phase excited during the interaction is illustrated.     

Solitons in a molecular chain with impurities

The propagation of Davydov's soliton in the molecular chain with an impurity has been investigated. The numerical analysis demonstrates that the presence of the impurity leads to the decreasing of the soliton velocity, as well as to the localization (pinning) of the excitation in a region of space close to the impurity or even to the reflection or destruction of the soliton. The analytical results which demonstrate that the influence of the impurity is equivalent to the existence of some localized external inhomogeneous field or friction force have been obtained also.     

Photons trapping within a nano-ring resonator controlled by light

We propose the interesting results that a bright and dark soliton pulse can be localized within a nonlinear nano-waveguide. The system consists of nonlinear micro- and nano-ring resonators, whereas the soliton pulse can be input into the system and trapped within the nano-waveguide. A soliton input is chopped by the nonlinear effects known as chaos into smaller pulses. The required pulse is filtered and amplified, which can be controlled and localized within the nano-waveguide. The localized bright and dark solitons are trapped within a nano-waveguide by controlling the nano-waveguide input power, which means that the photons trapping is controlled by light.     

具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化

运用变分法研究了具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化特性,分析了调谐囚禁电势对暗孤子运动的影响.结果表明,囚禁在调谐势阱中的暗孤子将振动,势阱强度和三体作用的符号影响了暗孤子的演化,并改变了BEC系统的振动特性.     

Landau dynamics of a grey soliton in a trapped condensate

It is shown that grey soliton dynamics in a one-dimensional trap can be treated within the framework of the local density approximation as Landau dynamics of a quasiparticle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass 2m. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively.     

Generation of Fundamental Dark Soliton Train in Positive Dispersion-decreasing Fibers

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具有局部畸变的常规势阱中玻色-爱因斯坦凝聚孤子的演化特性

运用数值模拟方法解Gross—Pitaevskii方程,研究了具有局部畸变（impurity）的常规势阱中玻色-爱因斯坦凝聚（BEC）孤子的演化特性,发现势阱的局部畸变对BEC孤子随时间演化的特性有重要影响,并且其影响与畸变的强度、势阱的幅度和势阱的类型有关。     

Calculations of localized modes on surface and impurity layer embedded in a semi-infinite Heisenberg ferromagnet

We investigate the magnetic excitations for the magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of an impurity layer embedded within a semi-infinite ferromagnet. A Heisenberg model is employed to investigate the possibility that localized modes can occur with an impurity layer implanted within a semi-infinite ferromagnet. No electronic effects are considered. The theoretical approach employs the matching procedure in the mean field approximation and determines the propagating and evanescent spin amplitude fields including the contribution due to an applied field. The results are used to calculate the energies of localized modes associated with the impurity layer and with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the impurity layer and surface modes. It is shown that more localized modes can occur and the modification of the spin wave spectra can be signaled by the appearance of surface and impurity modes, besides the bulk excitations. Also, the bulk spin fluctuations field, the spin waves localized on the surface as well as on impurity layer depend are shown to depend on the nature of the exchange coupling between spin sites, the values of spin sites and the position of the impurity layer from the surface.     

Motion of a Bose-Einstein Condensate Bright Soliton Incident on a Step-Like Potential

The motion characteristics of a Bose-Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross-Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potentiaI in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.     

Soliton evolution and control in a two-mode fiber with two-photon absorption

Soliton dynamics are numerically investigated in a two-mode fiber with the two-photon absorption, and the effects of the two-photon absorption on the soliton propagation and interaction are demonstrated in different dispersion regimes.Soliton dynamics depend strictly on the sign and magnitude of the group velocity dispersion(GVD) coefficient of each mode and the strength(coefficient) of the two-photon absorption. The two-photon absorption leads to the soliton collapse,enhances the neighboring soliton interaction in both modes, and increases the energy exchange between the two modes.Finally, an available control is proposed to suppress the effects by the use of the nonlinear gain with filter.     

Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.     

线性和二次电光效应共同主导的非相干耦合空间孤子族

基于加偏压的单光子光折变晶体,理论推导了线性和二次电光效应共同主导下的亮孤子族和暗孤子族的解,数值研究了亮孤子族和暗孤子族的强度包络和稳定特性,讨论了线性和二次电光效应在孤子族形成中的不同作用.结果表明:线性和二次电光效应的相互作用能够增强亮孤子族的光折变非线性,而减弱暗孤子族的光折变非线性.此外,在传输过程中,亮孤子族的各个分量能够稳定传输;暗孤子族各个分量在较长传输距离时表现出不稳定性.     

Nonautonomous Dark Solitons and Rogue Waves in a Graded-Index Grating Waveguide

We analytically present a family of nonautonomous dark solitons and rogue waves in a planar graded-index grating waveguide with an additional long-period grating.The dark solitons whose dynamics described by the explicit expressions such as the valley,background and wave central position are investigated.We find that dark soliton's depth and the long-period grating have effects on soliton's wave central position;the gain or loss term affects directly both the background and valley of the soliton.For rogue waves,it is reported that one can modulate the distribution of the light intensity by adjusting the parameters of the long-period grating.Additionally,more rogue waves with different evolution behaviors in this special waveguide are demonstrated clearly.     

无偏压的串联光折变晶体回路中高斯光束传播特性调节

根据串联光折变晶体回路中独立空间孤子对理论,研究了明暗孤子对之间的相互依赖特性.假设一束暗孤子波和一束高斯光束分别入射到回路中两块晶体上,利用数值计算方法讨论了改变其中暗孤子光束的强度对高斯光束在另外一个晶体中传播特性的影响.结果表明,调节暗孤子的强度能够影响高斯光束的传播特性,可以决定高斯光束在晶体中是否能够演化为稳定传播的明孤子波 关键词： 非线性光学 光折变效应 光折变空间孤子对 高斯光束     

Temperature effects of Hamiltonian dark solitons on the stability of holographic solitons in a separate holographic–Hamiltonian soliton pair

We investigate theoretically the temperature effects on the evolution and stability of a separate holographic–Hamiltonian dark–dark or bright–dark soliton pair formed in an unbiased serial photorefractive crystal circuit. Our numerical results show that, for a stable dark–dark or bright–dark soliton pair originally formed in a crystal circuit at given temperatures, when the crystal in which formed a Hamiltonian dark soliton changes, the holographic dark or bright soliton supported by the other crystal tends to evolve into another stable soliton or experiences larger cycles of compression or breaks up into beam filaments or exhibit a common decaying process. The holographic dark soliton is more sensitive to the temperature change than the holographic bright one.