强非局域空间光孤子在铅玻璃材料中的传输特性

本文研究了矩形和圆形截面铅玻璃介质中强非局域空间光孤子的传输特性.基于镜像法,光束在铅玻璃中的传输被分成独立的两个过程,即孤子的形成和孤子的整体偏转.孤子的形成不依赖于边界,它来源于入射源光束本身形成的折射率分布的作用,所以形成孤子的临界功率只与材料的性质和入射光束束宽有关.孤子的整体偏转在本质上来源于边界的作用,其偏转力在数值上等同于所有镜像光束与源光束之间的作用力.截面圆形和截面矩形的边界分别"镜像"出一个和无穷多个镜像光束,进而导致不同边界条件下孤子不同的偏转轨迹.文中解析求得的孤子的临界功率以及两 关键词： 空间光孤子 强非局域 镜像法 铅玻璃     

From electrostatics to optics: The study on the soliton propagation in lead glass using the image beams method

We investigate the soliton propagation in lead glass with rectangle boundary by the method of image beams. This method is the analogue of the electric image method which is used to solve the Poisson type equation. In the general case that the beam width is much smaller than the boundary size, the soliton formation and the soliton steering are analytically studied independently. The critical power of the soliton formation is boundary independent. The boundary effect only provides, for the soliton steering, the dynamic force which is equivalent to the force between the soliton beam and the infinite number of image beams. The closed-form steering trajectories of the solitons are in good agreement with the experimental results.     

Analytical Investigation of Soliton Solutions to Three Quantum Zakharov-Kuznetsov Equations

In the present paper, the two-dimensional quantum Zakharov-Kuznetsov(QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations.     

Analytical Investigation of Soliton Solutions to Three Quantum Zakharov-Kuznetsov Equations

In the present paper, the two-dimensional quantum Zakharov-Kuznetsov (QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations.     

随机双折射对光孤子传输影响的研究

利用对称分步傅里叶法,数值模拟了光孤子在双折射光纤中的传输特性,分析了孤子脉冲两正交偏振分量的群速度失配对孤子传输产生的影响.结果表明,当光纤的双折射较小时,两偏振分量的脉冲强度变化不大,孤子基本能够保形传输|当光纤的双折射较大时,两偏振分量脉冲很快展宽,强度迅速减小,孤子不能够保形传输|如果光纤的双折射具有随机性,孤子传输的两偏振分量脉冲强度会随着传输距离有强弱不规则的变化,但是两偏振分量的强度变化互相补充,合成强度没有太大的变化,孤子能够稳定的传输|孤子间没有相互作用影响的传输距离随着光纤随机双折射偏振分量群速失配的增大而变小|通过选择恰当的振幅比,传统的不等振幅法仍然能够有效地抑制孤子间的相互作用.     

Chiral Solitons in 1+2 Dimensions

This paper obtains the exact 1-soliton solution to the chiral nonlinear Schrödinger’s equation in 1+2 dimensions. Both constant coefficients and time-dependent coefficients are considered. The topological as well as bright soliton solutions are obtained. The soliton ansatz method is used to carry out the derivation of the soliton.     

Bright and dark solitons of the Rosenau-Kawahara equation with power law nonlinearity

In this paper, the topological (dark) as well as non-topological (bright) soliton solutions to the Rosenau-Kawahara equation with power law nonlinearity are obtained by the solitary wave ansatz method. A couple of conserved quantities are also calculated for the case of bright soliton solution.     

Solitons in photovoltaic photorefractive media with an external electric field

We use the classical Lie-group method for studying the evolution equation in photovoltaic photorefractive media with an external electric field, reducing it to some similarity equations firstly, and then obtain some exact analytical solutions including the soliton solution, the period solution and the oscillatory solution. We also obtain the bright soliton, dark soliton, gray soliton from these similarity equations with the numerical method. Furthermore, we investigate what factors contribute to the beamwidth of these solitons with the numerical method and know the beamwidth of these solitons are associated with the external electric field, the photovoltaic field and the intensity ratio of the incident soliton.     

利用光孤子机制实现超宽范围波长调谐的理论和实验研究

以获得光参量啁啾脉冲放大系统主激光与抽运光两种波长、宽带、超短脉冲的产生及精密同步为目标,探索采用光孤子机制实现超宽带宽范围的可调谐超短脉冲产生. 数值模拟了孤子传输过程中的时域-频域演化过程及与其他非线性效应的相互作用过程和特性. 实验验证了利用光孤子机制产生可调谐脉冲的方法. 同时还观察到孤子的形成、分裂、自频移等现象,在可见光到近红外波段都演示了波长可调谐的输出特性,并且与理论分析结果符合较好. 关键词： 光参量啁啾脉冲放大 可调谐脉冲产生 非线性薛定谔方程 孤子机制     

Bifurcations and new exact travelling wave solutions for the bidirectional wave equations

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional wave equations. The results presented in this paper improve the related previous studies.     

Dynamics of the Manakov Solitons in Biased Guest-Host Photorefractive Polymer

In the biased guest-host photorefractive polymer, the Manakov equations can be used to describe the optical soliton propagation and interaction. Hereby for such equations, via the Hirota method and symbolic computation, analytic soliton solutions in the bright-dark and dark-dark forms are obtained. Based on the choice of photorefractive polymer parameter and incident-optical-beam parameter, the bright-dark and dark-dark solitons as well as their interaction can occur in the polymer when the total intensity is much lower than the background illumination, and our analysis indicates that the incident light with different polarization directions influence little on the soliton propagation. γ, representing the soliton intensity far away from the soliton center, determines the appearance of bright or dark soliton under the background illumination. Through the graphic and asymptotic analysis on the two-soliton solutions along with the different γ, we find that there exist the elastic and inelastic interactions between the bright-dark solitons, while the interactions between the dark-dark solitons are always elastic.     

扩展的双曲函数法和Zakharov方程组的新精确孤立波解

借助于符号计算软件Maple，利用扩展的双曲函数法求出了Zakharov方程组的精确孤立波解，包括钟状孤立波解、扭结状孤立波解、包络孤立波解、奇性孤立波解和一种新的形式的孤立波解.这种方法也适用于其他非线性波方程.     

Effects of positron density and temperature on ion acoustic dressed solitons in an electron–positron–ion plasma

Ion acoustic dressed solitons in a three component plasma consisting of cold ions, hot electrons and positrons are studied. Using reductive perturbation method, Korteweg–de Vries (KdV) equation and a linear inhomogeneous equation, governing respectively the evolution of first and second order potentials are derived for the system. Renormalization procedure of Kodama and Taniuti is used to obtain nonsecular solutions of these coupled equations. It is found that electron–positron–ion plasma system supports only compressive solitons. For a given amplitude of soliton on increasing the positron concentration, velocity of the KdV as well as dressed soliton increases. For any arbitrary values of soliton's amplitude and positron concentration, velocity of the dressed soliton is found to be larger than that of the KdV soliton. For small amplitude of solitons, the width of KdV as well as dressed soliton decreases as positron concentration increases and width of dressed soliton is found to be larger than that of the KdV soliton. However, for a large value of soliton's amplitude as concentration of positrons increases, instead of decreasing width of dressed soliton starts to increase.     

在反常色散区艾里脉冲与光孤子相互作用规律的研究

本文采用分步傅里叶法,研究了在反常色散区孤子和艾里脉冲相互作用的规律,并且对相互作用后的孤子和艾里脉冲各自的强度、时域和时移进行了MATLAB仿真.通过仿真发现光孤子和艾里脉冲在光纤中相互重叠时,交叉相位调制(XPM)就会建立并且这种调制会影响孤子和艾里脉冲的性质.在相互作用过程中,孤子的形状保持不变,但是受到艾里脉冲自加速特性的影响孤子会发生偏移.艾里脉冲受XPM的影响会转化为孤子,传播方向也会发生偏移.可见,XPM使得艾里脉冲和孤子各自的性质都相互影响着对方.艾里脉冲和孤子的时域也会受到XPM的影响,使得原本不相同的脉冲形状都转变为含有一个主峰和一个次峰的相似结构,并且主峰和次峰的位置和脉冲宽度也大致相同,这也是艾里脉冲能够转换为孤子的一个依据.另外本文还模拟了不同输入强度r下的孤子和艾里脉冲的变化情况,模拟发现不管是艾里脉冲还是孤子时移都随着输入强度r的增大而增大,并且它们的变化趋势都是一样的,同时模拟还发现在相同的的r值下,时移也会随着a值的增大而增大.     

拉曼增益对孤子传输特性的影响

利用考虑拉曼增益效应的非线性薛定谔方程, 在忽略光纤损耗的情况下, 采用基于MATLAB的分步傅里叶数值算法, 得出线性算符和非线性算符具体的表达式, 分步作用于光孤子脉冲传输方程, 仿真模拟了光孤子在光纤中传输时的演变. 与不考虑拉曼增益的光孤子在光纤中传输相对比, 探析了拉曼增益对孤子传输特性的影响.拉曼增益会破坏孤子的传输周期, 导致孤子在光纤中传输时快速衰减, 并且影响程度和输入孤子的脉冲峰值功率大小有关, 拉曼增益对基态孤子和高阶孤子的影响也不相同. 关键词： 拉曼增益 孤子 对称分步傅里叶法 非线性薛定谔方程     

Effects of dark soliton crystal temperature on the self-deflection of bright soliton in a biased serial photovoltaic photorefractive crystal circuit

Based on the theory of one-dimensional separate soliton pairs formed in a serial photovoltaic photorefractive crystal circuit, the effects of the dark soliton crystal temperature on the self-deflection of the bright one in a bright-dark soliton pair are investigated. The numerical results indicate that the spatial shift of the bright soliton can experience obvious increase in their self-deflection with the increase of the temperature of the dark soliton. The self-bending process is further studied using perturbation techniques and the results are found to be good agreement with that obtained by numerical method.     

(3+1)维Burgers系统的新精确解及其特殊孤子结构

将改进的Riccati方程映射法和变量分离法推广到(3+1)维Burgers系统,得到了该系统的新显式精确解.根据得到的孤波解,构造出Burgers系统的几种特殊孤子结构,例如柱状孤子、状孤子和内嵌孤子等,研究了孤子间的相互作用. 关键词： 改进的映射法 (3+1)维Burgers系统 孤子结构 相互作用     

A simple and direct method for generating travelling wave solutions for nonlinear equations

We propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method.     

Chiral Solitons With Time-Dependent Coefficients

This paper obtains the exact 1-soliton solution to the chiral nonlinear Schrödinger’s equation with time-dependent coefficients. Both bright and dark soliton solutions are obtained. The soliton ansatz method is used to carry out the derivation of the soliton.     

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.