Slowly moving matter--wave gap soliton propagation in weak random nonlinear potential

We systematically investigate the motion of slowly moving matter--wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross--Pitaevskii equation.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

有限宽度布拉格原子层中光子囚禁与移动孤子的研究

研究二能级原子层宽度对一维共振吸收布拉格反射镜中自感应透明光孤子形成的影响.结果表明：在有限宽度的二能级原子层中仍可激发稳定的移动孤子，其激发条件对原子层宽度依赖不大；然而静止孤子的存在条件却敏感地依赖于原子层的宽度，二能级原子层宽度只有小于某一特定值时，光脉冲才能演化成静止孤子. 关键词： 有限宽度 周期结构 移动孤子 静止孤子     

Oscillation of spatial solitons in a waveguide with a symmetrical refractive index profile

Dynamics of (1+1)D spatial solitons in a Kerr medium with a transversely symmetrical refractive index profile is investigated. Propagation of solitons is analysed theoretically by using an effective-particle approach. Analytical results show that the soliton oscillates periodically with a variable acceleration. The expression of oscillatory period is derived by introducing a concept of `average acceleration'. Both acceleration and oscillatory period are determined by the parameters of the input soliton and the waveguide. Propagations of solitons are simulated numerically and good agreement is obtained between the theoretical and numerical results.     

Gap solitons and their linear stability in one-dimensional periodic media

An analytical theory utilizing exponential asymptotics is presented for one-dimensional gap solitons that bifurcate from edges of Bloch bands in the presence of a general periodic potential. It is shown that two soliton families bifurcate out from every Bloch-band edge under self-focusing or self-defocusing nonlinearity, and an asymptotic expression for the eigenvalues associated with the linear stability of these solitons is derived. The locations of these solitons relative to the underlying potential are determined from a certain recurrence relation, that contains information beyond all orders of the usual perturbation expansion in powers of the soliton amplitude. Moreover, this same recurrence relation decides which of the two soliton families is unstable. The analytical predictions for the stability eigenvalues are in excellent agreement with numerical results.     

Surface superlattice solitons in nonlocal nonlinear media

We analyse surface solitons at the interface between a one-dimensional photonic superlattice and a uniform medium with weak nonlocal nonlinearity. We demonstrate that in deep lattices there exist three kinds of surface solitons when the propagation constant exceeds a critical value, including two on-site solitons and one off-site soliton. These three kinds of surface solitons have unique dynamical properties. If the relative depth of the superlattice is low, there is only one kind of off-site soliton; however, the solitons of this kind can propagate stably, unlike their deep superlattice counterparts. Dipole surface solitons are also investigated, and the stable domain is given.     

非线性光纤耦合器孤子传输的相敏能量交换特性

从动力学的角度出发,分析了非线性双芯光纤耦器中不同芯层内孤子脉冲的相位对能量交换特性的影响,只要初始注入孤子信号的相位差选择恰当。     

Controlling the collision between two solitons in the condensates by a double-barrier potential

We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method.In the linear case,we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence.For weak nonlinearity,it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties.Especially,in the case of regarding a double-barrier potential as the output source of the solitons,the collision spots between two dark solitons can be controlled by the height of the barrier potential.     

Spatial solitons in photonic lattices with large-scale defects

We address the existence,stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium.Several families of soliton solutions,including flat-topped,dipole-like,and multipole-like solitons,can be supported by the defected lattices with different heights of defects.The width of existence domain of solitons is determined solely by the saturable parameter.The existence domains of various types of solitons can be shifted by the variations of defect size,lattice depth and soliton order.Solitons in the model are stable in a wide parameter window,provided that the propagation constant exceeds a critical value,which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium.We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.     

The appearance of gap solitons in a nonlinear Schrödinger lattice

We study the appearance of discrete gap solitons in a nonlinear Schrödinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q=π/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this “nonlinear gap boundary” are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gap edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.     

Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity

Oscillatory behavior of spatial solitons in a transverse parabolic gradient refractive index distribution (GRIN) waveguide with both local and nonlocal nonlinearity is investigated. Dynamics of such solitons are analyzed by the effective-particle approach method. For weak nonlocal nonlinearity, solitons oscillate in transverse direction periodically during propagation. The normalized width and maximum of refractive index variation of the waveguide play a key role in determining the oscillating period while the position of soliton oscillatory center is slightly influenced by the nonlocal nonlinearity. Stronger nonlocal nonlinearity leads to instability of the oscillatory solitons. Furthermore, the dynamics of the solitons are simulated numerically and good agreements are obtained between the analysis and numerical results. This behavior may be used in all-optical routers, switches etc. PACS 42.65.Tg; 42.65.Jx; 42.65.Wi     

Ion-acoustic solitons in multispecies spatially inhomogeneous plasmas

Ion-acoustic solitons are investigated in the spatially inhomogeneous plasma having electrons-positrons and ions. The soliton characteristics are described by Korteweg-de Vries equation which has an additional term. The density and temperature of different species play an important role for the amplitude and width of the solitons. Numerical calculations show only the possibility of compressive solitons. Further, analytical results predict that the peak amplitude of soliton decreases with the decrease of density gradient. Soliton characteristics like peak amplitude and width are substantially different from those based on KdV theory for homogeneous plasmas     

Matter-wave bright solitons: Internal atomic recombination and external feeding

We consider matter-wave bright solitons in the presence of three-body atomic recombination, an axial periodic modulation and a feeding term, and use a variational method to derive conditions to have dynamically stabilized solitons due to compensation between the dissipation and alimentation of atoms from external sources. We critically examine how the BEC soliton is affected by the imbalance between the internal atom loss and external feeding. We pay special attention to study the influence of these terms on the soliton dynamics in optical lattice potentials that cause periodic modulation.     

Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We investigate the moving matter-wave solitons in spin-orbit coupled Bose-Einstein condensates(BECs) by a perturbation method.Starting with the one-dimensional Gross-Pitaevskii equations,we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spinorbit coupling.The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs.We find different types of moving solitons:dark-bright,bright-bright and dark-dark solitons.Interestingly,moving dark-dark soliton for attractive intra- and inter-species interactions is found,which depends on the Raman coupling.The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin-orbit coupling.     

Symmetric and antisymmetric vector solitons for the fractional quadric-cubic coupled nonlinear Schrödinger equation

The fractional quadric-cubic coupled nonlinear Schrödinger equation is concerned, and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method. The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated. Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index, respectively. The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied. Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.     

Multi-Solitons and Combined Solitons with Self-Similar Behaviors in a Birefringent Fiber with Higher-Order Effects

A coupled variable-coefficient higher-order nonlinear Schr(o|¨)dinger equation in biretringent fiber is studied,and analytical multi-soliton,combined bright and dark soliton,W-shaped and M-shaped soliton solutions are obtained.Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed,and the decaying or increasing,even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.     

Two-dimensional vector solitons in a cold atomic gas via electromagnetically induced transparency

We investigate the formation and propagation of vector vortex solitons (VSs) and unipolar solitons (USs) in a cold coherent atomic gas with a Bessel lattice (BL). The system considered is a gas with a tripod level configuration. Owing to the big enhancement of Kerr nonlinearity contributed by the electromagnetically induced transparency (EIT), a weak vector vortex soliton can be effectively formed with ultraslow propagation velocity. We also demonstrate that the characteristics of two-dimensional VSs and USs can be controlled and manipulated by adjusting the parameters of BL. Results obtained may be useful for designing all-optical switches at low light levels.     

饱和对数非线性介质中非相干孤子碰撞对相干性的改善

基于相干密度理论，数值地研究了饱和对数非线性支持的部分非相干亮孤子对的相互作用.研究表明，两个非相干亮孤子碰撞不仅能增大碰撞区的光强，还可以大大改善部分非相干光束的相干性.同时还研究了非相干性对孤子碰撞的影响，非相干性不仅抑制了孤子间的相干作用如吸引、排斥和能量交换，同时还由于非相干叠加作用而引入了弱的相互吸引. 关键词： 非相干性 饱和对数非线性 空间光孤子     

超常介质中暗孤子的形成和传输特性研究

利用一种扩展的双曲函数级数方法求解超常介质中的传输方程，得到了各种不同情形下的暗孤子解，分析了可控自陡效应和二阶非线性色散效应对孤子形成和传输特性的影响.结果表明，超常介质中负的自陡效应使得暗孤子的中心位置随传输距离向脉冲前沿方向漂移，与常规介质中自陡效应(恒为正)的作用相反；特别是，由于二阶非线性色散的作用，使得在没有线性群速度色散的情形下同样可形成孤子，而且在反常线性色散情形也可形成暗孤子.