Small amplitude dust-acoustic soliton energy in dusty plasmas with suprathermal polarization force

The effect of suprathermal polarization force on both linear and weakly nonlinear dust-acoustic solitary structures in a three-component dusty plasma is investigated. For this purpose, a new expression of the polarization force acting on dust particles that include the electronic suprathermal effect is derived. The results are applied to two different experimental dusty plasmas. We have found that the polarization force acting on the dust grains decreases as the electron suprathermality becomes more significant. In addition, we have shown that, for a given value of the spectral index κ , the polarization force magnitude fluctuates from one plasma to another. The changes arising in the propagation of small-amplitude dust-acoustic (DA) solitons due to the presence of this suprathermal polarization force are also analysed. Interestingly, an increase in the magnitude of the polarization force leads to an increase in the amplitude and width of DA soliton and provides more energy to the motion of this soliton.     

Darboux transformation and exact multisolitons for a matrix coupled dispersionless system

We present a matrix coupled dispersionless(CD) system. A Lax pair for the matrix CD system is proposed and Darboux transformation is constructed on the solutions of the matrix CD system and the associated Lax pair. We express an N soliton formula for the solutions of the matrix CD system in terms of quasideterminants. By using properties of the quasideterminants, we obtain some exact solutions, including bright and dark-type solitons, rogue wave and breather solutions of the matrix CD system. Furthermore, it has been shown that the solutions of the matrix CD system are expressed in terms of solutions to the usual CD system, sine-Gordon equation and Maxwell-Bloch system.     

Orientation dependence in high harmonics of ZnO with polarization corrections to counteract the birefringent effect

We investigate the influence of the birefringence on the high-order harmonics in an a-cut Zn O crystal with midinfrared laser pulses. The high harmonics exhibit strong dependence on the alignment of the crystal with respect to the laser polarization. We introduce the Jones calculus to counteract the birefringent effect and obtain the harmonics with polarization corrections in Zn O. We show that the birefringent effect plays an important role in the orientation dependence of HHG.     

一类具有多个偏差变元的高阶中立型微分方程的周期解

利用Mawhin重合度理论,获得了一类具有多个偏差变元的高阶中立型微分方程(x(t)-cx(t-r))~(l)+h(x(t))x′(t)+■α~i(t)f(x′(t-μ_i(t))+■β_j(t)g(x(t-τ_i(t)))=p(t)周期解存在性的新结果,推广和改进了已有文献的相关结果.     

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin–orbit coupled Bose–Einstein condensate

We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling. With the modulation of the spin–orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin–orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin–orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.     

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.     

一维守恒的Lagrangian ADER格式

基于欧拉框架下ADER格式,构造一维守恒只有一个时间步的、高精度中心型拉格朗日ADER(LADER)格式.构造r阶LADER格式包括:从欧拉方程出发推导拉格朗日框架下积分形式的方程、采用WENO方法高精度重构节点处守恒量和从1阶到r-1阶的空间导数、求拉氏框架下这些变量的Godunov值,并计算1阶到r-1阶的时间全导数,最后高精度离散积分形式的流通量函数.对光滑流场的模拟表明,LADER格式达到设计的精度;对含强间断的流场模拟表明,数值解在间断附近基本无振荡.     

利用双色啁啾激光场产生超短的单个阿秒脉冲

数值研究了氦原子在两束啁啾激光场形成的组合场驱动下所发射高次谐波的特点.计算结果表明,当两束啁啾激光场的形式为δi(t)=-βiωit2/T (i=1,2)并且啁啾参数分别为β1=0.3和β2=0.6时,高次谐波谱的平台区域能得到很大的扩展,随后通过激光场强度以及相位的优化,谐波截至能量延伸到了812eV.最后通过叠加谐波次数从160次到210次,210次到260次,260次到310次,可获得一系列脉宽为33as的单个阿秒脉冲.     

(1+2)维强非局域空间光孤子的相互作用

强非局域空间光孤子是指满足强非局域条件的空间孤子.在Snyder和Mitchell工作的基础上，获得了不共面对称斜入射(1+2)维强非局域空间光孤子对相互作用问题的精确解析解.结果表明，光束初始中心距离在大范围尺度内变化时，双孤子的演化都能形成类似DNA结构的稳定缠绕，这种稳定缠绕的结构与双孤子的初始相位差无关；光束中心在横截面上的投影轨迹一般是一个斜椭圆，通过改变两光束的初始中心距离和倾斜度可以控制该椭圆轨迹的变化.指出了利用(1+2)维强非局域空间光孤子的相互作用特性实现平面全光开关和全光互联的潜在可能性. 关键词： (1+2)维非局域非线性介质 空间光孤子的相互作用 全光开关 全光互联     

A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes

Analytical solutions are obtained for a coupled system of partial differential equations involving hyperbolic differential operators. Oscillatory states are calculated by the Hirota bilinear transformation. Algebraically localized modes are derived by taking a Taylor expansion. Physically these equations will model the dynamics of water waves, where the dependent variable (typically the displacement of the free surface) can exhibit a sudden deviation from an otherwise tranquil background. Such modes are termed ‘rogue waves’ and are associated with ‘extreme and rare events in physics’. Furthermore, elevations, depressions and ‘four-petal’ rogue waves can all be obtained by modifying the input parameters.