Korteweg-de Vries方程的准孤立子解及其在离子声波中的应用

应用推广的tanh函数展开法,给出了Korteweg-de Vries方程具有准孤立子行为的两组孤子-椭圆周期波解,其中一组为新解.推导了均匀磁化等离子体中描述离子声波动力学行为的Korteweg-de Vries方程,发现电子分布、离子电子温度比、磁场大小、磁场方向对离子声准孤立子的波形具有显著影响.     

开路光伏空间孤子的动态行为

从理论上研究了开路情况下一维光伏空间孤子的时间演化过程.采用数值方法,通过研究有无背景光辐照下光伏空间亮(暗)孤子的含时空间电荷场,分别得到了光伏空间亮(暗)孤子的孤子波形强度微分方程.在此基础上研究了开路情况下通过增加均匀背景光辐照强度对光伏空间孤子及其半峰全宽的影响.结果显示,通过增加均匀背景光辐照强度,光伏空间孤子随时间的演化过程比没有均匀背景光时加快的倍数为均匀背景光强与暗辐照光强之比.光伏空间孤子的半峰全宽达到稳态所需的时间随孤子峰值强度和暗辐照与均匀背景光强度之和的比值的增大而变短.     

无偏压光伏晶体中的非相干耦合亮暗孤子对及其传输特性

理论研究了均匀照明的无偏压光伏晶体中非相干耦合亮暗光伏孤子对的存在性.发现在共同的光伏光折变效应作用下,具有相同偏振和波长但彼此互不相干的两光束可以形成非相干耦合亮暗光伏孤子对.推导了亮、暗光场分量及其半峰全宽(FWHM)的表达式,并以Cu:KNSBN为例讨论了光强分布特性及半峰全宽与孤子光强的变化关系.结果表明,在形...     

光传输、通信理论

当皮秒孤子在群色散沿长度方向指数衰减的色散渐变光纤(DDF)中传输时,孤子的群色散和自相位调制保持局域平衡.宽度可以保持不变,用于孤子光通信有其特殊的优越性。但群色散分布满足要求的色散渐变光纤制造难度较大。文章提供了用群色散分段均匀的光纤(称其为阶梯色散渐变光纤)来加以替代的可能性。模拟结果表明,孤子可以在由这样的光纤及滑频滤波器     

单离子各向异性影响下的一维铁磁链中的孤子

利用行波解法，研究了考虑交换各向异性和单离子各向异性的一维铁磁链，得出椭圆函数波解和孤子解,并讨论了单离子各向异性对椭圆函数波和孤子的影响.研究表明：单离子各向异性对一维铁磁链中椭圆函数波和孤子的激发及其稳定性有显著影响.单离子各向异性不利于易轴铁磁链中椭圆函数波和孤子解的激发，但有利于它们的稳定；而在易平面铁磁链中，单离子各向异性使椭圆函数波和孤子激发变得容易，但不利于它们的稳定.此外，还讨论了单离子各向异性对一维各向同性铁磁链中的孤子激发具有的影响. 关键词： 各向异性 单离子各向异性 孤子 铁磁链     

槽中双孤子互作用的微扰求解

孤子运动的Miles方程是一个具特征的非线性Schrdinger型方程.借求孤子解的微扰法,导出所遵循的矩阵方程,和孤子解的修正量δu(x,λ).并据双孤子解,计算了它的周期互作用状态 关键词： Miles方程 微扰双孤子解     

非均匀系统中非自治孤子的色散和非线性管理

基于包含自发拉曼散射和外电光调制效应的非自治非线性薛定谔方程,采用简单的变换方法,解析研究了三种非均匀系统中非自治孤子的管理和传输。结果发现,在非均匀的非线性渐增或色散渐减光纤系统中都存在精确的啁啾非自治孤子解,都可以实现孤子的放大和压缩,但具有不同的速度、频移和啁啾特性;而在非均匀的色散和非线性均渐减光纤系统中,可以支持无啁啾的非自治孤子,该孤子具有不变的脉宽和振幅以及振荡衰减的速度,孤子的频移仅由自发拉曼散射决定。同时,数值模拟结果进一步证实在三种非均匀管理系统中都可支持非自治孤子的传输。该研究结果为实际非均匀孤子管理系统中实现孤子的压缩和传输提供了理论依据。     

变系数拉曼增益对两种特殊形式暗孤子传输特性的影响

在非均匀光纤中,基于带有分布色散,自相位调制和自陡峭的变系数修正非线性薛定谔方程(VcMNLSE)及其两种暗孤子解,详细讨论了不同形式的拉曼增益对暗孤子解传输特性的影响。结果表明:周期的正弦函数拉曼增益会使两种暗孤子解的背景波产生周期性振荡,并且振荡周期和幅度均随正弦函数的参数变化而变化;双曲正弦函数和指数函数的拉曼增益将会使两种暗孤子解的背景波功率升高;正切函数的拉曼增益会使两种暗孤子解的背景波产生阶跃性变化,且周期振荡暗孤子解会在传输过程中发生分裂。     

光通信

光传输、通信理论 TN911 2004021404 具有周期非均匀扰动的色散管理系统中的孤子传输=Soliton propagation in a dispersion-managed system with periodically inhomogeneous perturbations[刊,中]／殷德京(湖北师范学院物理系．湖北,黄石(435002)),李宏∥光子学报．—2003,32(6)．—718-722 在准理想的色散管理系统中建立了非均匀扰动模型,研究了它们对孤子传输和相互作用的影响。这些扰动导致孤子崩塌,加剧了孤子间相互作用。它们影响的大小与周期长度和扰动强度有关,并且存在最坏周期长度和扰动共振现象。最后,引入非线性增益和滤波器来有效控制这些扰动的影响。图7参12(严寒)     

在MOCVD外延生长中V/Ⅲ比对Al_xGa_(1-x)As外延层中A1组分分布的影响

本实验首次观察到用MOCVD方法在GaAs基片上外延生长Al_xGa_(1-x)As/GaAs薄膜结构时,生长中所用的Ⅴ/Ⅲ比对外延层中Al组份x的分布的影响.当Ⅴ/Ⅲ比较低时,外延层中的Al组份出现很明显的层状阶梯形三层分布:靠近基片的一层中x值较低,而在外延层的表面层中x值较高.随着生长中所用的Ⅴ/Ⅲ比增加时,Al组份的分布趋于均匀.利用GaAs的高温热分解和Ga、As离子在晶体中的热扩散及其对外延生长的影响,对这一现象作了初步解释.     

Line soliton interactions of the Kadomtsev-Petviashvili equation

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line solitons as y-->-infinity. We also show that the (2N-1)!! types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.     

The Exact Solutions of Some (2 + 1)-Dimensional Integrable Systems

The equivalence of three (2 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.     

Influence of Spectral Filtering and Nonlinear Gain on an Optical Soliton

Using the direct soliton perturbation theory, we investigate the evolution of soliton parameters and the firstorder correction of bright soliton in a system with linear and nonlinear gain （or loss） and spectral filtering in a comprehensive way. The results obtained by means of our analytic method are consistent with numerical simulations. It is also found that the stable soliton propagation which has been investigated in a previous report by others is the limit case of our results.     

The Exact Solutions of Some (2+1)-Dimensional Integrable Systems

The equivalence of three (2+1)-dimensional soliton equations is proved, and the quite general solutions with some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many special types of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutions are obtained.     

Structures and Interactions of Soliton in (2+1)-Dimensional Generalized Nizhnik-Novikov-Veselov Equation

A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.     

On the Dromion Solutions of a (2+l)-Dimensional KdV-Type Equation

A general curve soliton which is finite on a curved line and localized apart from the curve for a (2+1)-dimensional KdV-type equation is found. For the KdV-type equation, we find that the dromion solutions can be obtained not only by two perpendicular line solitons, two nonperpendicular (with one is parallel to x-axis) line solitons, but also by one line soliton and one curve soliton. Various types of multi-dromion solutions which are constituted by n straight line solitons parallel to the x axis and one curve soliton can be cast in a simple formula with two arbitrary functions. The KdV-type equation is not integrable because it cannot pass through the three nonparallel line soliton test.     

Soliton molecules and the CRE method in the extended mKdV equation

The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition, which is called velocity resonance. One soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable parameters. The soliton molecules including the bright and bright soliton, the dark and bright soliton, and the dark and dark soliton are exhibited in figures 1–3, respectively.Meanwhile, the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevé method. The consistent Riccati expansion(CRE) method is applied to the extended mKdV equation. It demonstrates that the extended mKdV equation is a CRE solvable system. A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method.     

Thermodynamics of solition configurations in a two-dimensional model for displacive phase transition

A mean field theory of soliton contribution of two-dimensional scalar field ₄–₂ into the partition function is developed. Interacting two-dimensional soliton configurations (SC) are imitated as charged contours coupled through a massive field. A thermodynamics of these contours is considered with the help of integration over an auxiliary field. It is shown that the soliton excitations are responsible for the phase transition but not the phonon excitations even in the displacive limit.     

色散缓变光纤的非线性啁啾效应

由于光孤子在光纤中传输受到啁啾效应等多种因素的影响 ,使孤子脉宽展宽 ,光脉冲在终端变得不可检测 ,严重影响误码率 ,所以研究不同因素对孤子脉宽的影响有其重要意义。本文求解了色散缓变光纤中含频率非线性啁啾效应的NLS方程 ,由得到的孤子解讨论了非线性啁啾效应和色散缓变效应对孤子脉宽的影响 ,由此说明 ,色散缓减效应等效长距离分布参数光纤放大器的增益 ,它导致非线性效应增加 ,孤子进一步被压缩 ,非线性啁啾效应使孤子在z值较小时 ,其脉宽收缩 ,在z值较大时又使孤子脉宽展宽。     

New Exact Solutions of （1 ＋ 1）-Dimensional Coupled Integrable Dispersionless System

This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed.