Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure.The characteristics of these breathing structures can be described by breathing frequency ?, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

Reflection-Transmission Transition of Bright-Bright Solitons Collision in Two Species Condensates with Repulsive Interspecies Interactions

Considering repulsive interspecies interactions,we study the dynamical properties of bright-bright solitons in two species Bose-Einstein condensates by using a variational approach combined with numerical simulation.It is shown that the interactions between bright-bright solitons vary from repulsive to attractive interactions with the increasing their separating distances,and at equilibrium position the bright-bright solitons are localized.Interestingly,a transition from reflection-to transmission-collision is firstly observed,different from previous results of only reflection collision appearing there.These results will be helpful for the experimental manipulating such solitons.

Effect of initial linear chirp on collision characteristics of two solitons in the birefringent fibre

The collision characteristics of the orthogonally polarized solitons with initial linear frequency chirp in the linear birefringent fibre for β2 〈 0 are numerically studied. It is found that initial chirp changes the threshold value of solitons to form the bound-state in the birefringent fibre. The effect of initial positive chirp on the threshold value is more obvious than that of negative chirp. In the case of （δ= 0.7 and initial interval 2τ0 = 1.25, the two solitons are mutually bound for 0.2 ≤ C ≤ 1, and they do not form the bound-state for -1 ≤ C 〈 0.2. Frequency shifts increase with the increase of chirp parameter C for -1 ≤ C 〈 0.2, and have the oscillatory structure for C ≥ 0.2. The effect of positive chirp on temporal FWHM is greater than that of negative chirp. The peak of temporal waveform oscillates with the propagation distance. The period and amplitude of the oscillation for the chirped case are greater than those for the unchirped case, and they vary with the increase of ｜C｜. The peak of output temporal waveform can be controlled by changing the initial chirp.

Head-on collision of ring dark solitons in Bose-Einstein condensates

The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.

Collision difference between Kerr spatial solitons and nonlinear Kerr spatial solitons

In order to study the collision of the Kerr solitons and the collision of the the nonlinear Kerr solitons,numerical simulation is employed and it is found that the collision of solutions is different.The collision of Kerr solution is periodically elastic while the collision of the the nonlinear Kerr solution is strongly inelastic.Periodic collisions of the Kerr solitons can be changed by changing the relative amplitude while the collisions of nonlinear the Kerr solitons can be adjusted by selecting the appropriate relative phase.

Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.

Collision induced splitting of bright soliton in Bose-Einstein condensate

This paper studies the collision dynamics of bright soliton in Bose-Einstein condensate with trapezoid potential. It is found that besides the total reflection and total transmission, one bright soliton can be divided into two bright solitons with different amplitudes in a controllable manner.

Soliton—Like Pulses in Vertical Granular Chain Under Gravity：Particle—Like or Wave—Like

We numerically study the propagation, reflection and collision of soliton-like pulses in the vertical granular chain under gravity. For the pure granular chain system, during the propagation and reflection processes at the fixed end, it behaves like a particle. When it is reflected at the free end, it behaves as neither particle-like nor wave-like.When the strengths of the two colliding soliton-like pulses are close, they collide just like particles. When their strengths are greatly different, they collide just like waves. For the soliton behavior in the collision process, from particle-like to wave-like, there is a critical value θC for the ratio θ of the strengths of the two initial pulses. For the two-layer granular chain, if the mass of the grains in the second layeris less than that in the first layer, the soliton-like pulse in the first layer usually excites about [1/m] soliton-like pulses in the second layer.

Nonlinear Interactions of Dispersion-managed Soliton in OTDM Systems

The dispersion-managed soliton (DMS) transmission model of dispersion-managed systems is established,and the intrachannel DMS interactions equation is obtained.The impact of soliton interactions on DMS systems are numerically investigated.Finally,the relationships of the collision length changing with map strength are revealed.

第一类导数非线性Schrdinger方程的高阶差分格式

利用Taylor展开法,给出了求解第一类导数非线性Schrdinger方程的五点四阶有限差分格式,该格式在空间上保持4阶精度,在时间上保持2阶精度。为了观察格式的适用性,将格式推广到了5阶Kd V方程。数值算例比较了该格式与Crank-Nicolson格式,验证了格式的精度阶,并给出了2个单孤子碰撞的数值模拟。

Toda晶格方程的双孤子解及其碰撞研究

对Toda晶格方程单孤子解进行推广,用待定系数法求得了双孤子解,并借助数学软件Mathematica研究了特定双孤子的碰撞行为.

波分复用孤子通信系统容量研究

在波分复用（ＷＤＭ）孤子通信系统中，不同信道的孤子由于载波频率不一样而会发生周期性的碰撞，碰撞将引起孤子到达接收端时间的移动，这个现象限制着邻近信道的最小频率间隔和可以被复用的最大频率范围，即决定了ＷＤＭ孤子通信系统的最大通信容量。

波分复用孤子系统中孤子碰撞特性研究

从耦合非线性薛定谔方程组出发,利用对称分步傅里叶方法,对波分复用孤子系统中两个不同波长孤子间的相互碰撞特性进行了数值研究。结果表明,碰撞会导致孤子脉冲的瞬间速度发生变化,孤子中心频率还将发生偏移,而且频率偏移量的大小与孤子的相对速度有关。

双折射光纤中孤子碰撞的数值研究

对双折射光纤中正交极化孤子碰撞进行了详细的数值计算和分析．对比文献［１］，发现在俘获态和分离态之间存在一种过渡态．

耦合薛定谔模型在光纤传导中的应用

薛定谔方程在光纤通信领域应用较为普遍与重要,本文主要针对一个高维耦合的薛定谔方程进行研究,先是给出了该高维耦合薛定谔方程的物理意义与应用背景,然后从光纤在传导中的无损传导现象出发,依据双线性方法探究了该耦合方程的孤子形式的解,并且借助符号计算根据孤子解的图像讨论了该薛定谔方程孤子解的传播过程。耦合薛定谔方程中存在孤子解之间的弹性碰撞,这在信号放大和光开关的研究中具有重要的意义,在通信系统中改善光传输系统方面的也有很多的应用。

Effect of Nonlinearity on Scattering Dynamics of Solitary Waves

We discuss the effect of nonlinearity on the scattering dynamics of solitary waves. The pure nth power model with the interaction potential V （Х） = Х^n/n is present, which is a paradigm model in the study of solitary waves. The dependence of the scattering property on nonlinearity is closely related to the topological structures of the solitary waves. Moreover, for one of the four collision types, the rates of energy loss increase with the strength of nonlinearity and would reach 1 at n ≥ 10, which means that the two solitary waves would become of fragments completely after the collision.

玻色-爱因斯坦凝聚体中孤子正碰及相移的研究

采用推广的PLK(Poincare-Lighthill-Kuo)方法研究二维盘状玻色-爱因斯坦凝聚体(BEC)中孤子的正碰,得到了2个描述暗孤子及其传播的KdV方程和孤子正碰引起的相移.与准一维柱状BEC中孤子正碰的相移结果进行比较发现:当波数取1时,二维平面上孤子正碰后发生的相移与一维柱线上孤子正碰后发生的相移近似相等.

非线性左手介质中波包相同孤子的碰撞

对于耦合非线性Schrdinger方程组所确定的波包相同的孤子,由于它们之间在非线性左手介质中的碰撞行为对这类孤子在该介质的传播具有重要的意义,因此,采用分步傅里叶方法对这种碰撞过程进行了数值仿真.仿真结果表明,两个孤子碰撞后能够保持其各自原有的特性,如形状和速度等.因在耦合非线性Schrdinger方程组的推导过程中已忽略了损耗,因此传播过程没有能量损失,分离后孤子的幅度、宽度也均没有发生变化.仿真结果有助于人们了解非线性左手Kerr介质中孤子的传播特点和碰撞行为.

Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects

In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincaré-Lighthill-Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail,