稳态光折变空间孤子传输的量子理论

稳态光折变空间孤子系统可用奇异Lagrange量描述，系统含Dirac约束.通常按对应原理写 出孤子系统的量子对易关系和量子运动方程时，未计及约束.对稳态光折变空间光孤子约束 系统进行Dirac括号量子化，给出了系统的对易关系和量子场方程.在线性近似下给出量子 非线性薛定谔方程的微扰解，并讨论了孤子的压缩性质. 关键词： 量子场论 量子光学 光折变空间孤子 压缩效应     

基于变系数3+1维三次-五次复金兹堡-朗道方程的亮孤子及混合孤子传输特性

变系数3+1维三次-五次复金兹堡-朗道(CGL)方程作为光孤子传输模型,不仅用五次项解释了现有模型所没有的物理意义,还拥有高维系统较低维系统更为丰富的非线性动力学特性.本文利用修正的Hirota方法,得到了变系数3+1维三次-五次CGL方程的解析孤子解.通过对非线性系数和光谱滤波项选取特定的参数,得到了一种特殊的混合孤子.分别讨论了改变非线性、光谱滤波和线性损失参数以及其他参数对孤子传输特性的影响,实现了对亮孤子和混合孤子传输的有效控制.本文结论对高维CGL系统在理论和实验研究方面具有一定的参考价值.     

非线性延时修正光纤孤子方程的稳态解问题Ⅰ.静态扭结孤波解

严格求解含非线性延时修正光纤孤立子方程,得到一类完全不同于光纤中已知的亮孤子和暗孤子的新型光学孤波解,并讨论了其物理含义及在光纤实验中观察这种扭结孤波的可能性。     

耦合复变系数Ginzburg-Landau方程的啁啾类孤波对传输特性研究

通过对耦合复变系数Ginzburg-Landau方程所描述的非线性光纤系统的研究,分别数值分析了啁啾类亮-暗和啁啾类暗-暗两组孤波对在这种非线性光纤中传输的稳定性.在加入非线性增益(损耗),和增益带宽限制放大(滤波的谱限制)效应后,耦合啁啾孤子对的特点是暗孤波在反常群速度色散区,亮孤子在正常群速度色散区时可以稳定传输.并进一步讨论了加入振幅微扰和白噪声微扰对孤子传输稳定性的影响.     

广义五阶KdV方程的孤波解与孤子解

利用求解非线性代数方程组的吴文俊特征列方法,借助计算机代数系统获得了一类较广泛的五阶非线性演化方程的孤波解和孤子解,修正和完善了已知的结论 关键词： 五阶KdV方程 孤波 孤子解     

光纤中飞秒孤子传输的量子理论

导出了光孤子系统的微观哈密顿量,用所给哈密顿量及色散关系导出了飞秒孤子在光纤中传输所满足的修正非线性薛定谔方程,用Hartree近似方法求解了所得方程,并研究了孤子的量子特征及经典过渡。结果表明,光纤中光场算符的量子力学平均为一系列有修正项的经典孤子的叠加,光场算符的准概率密度呈自压缩效应,压缩效果与高阶项的大小有关。 关键词：     

(2+1)维非线性KdV方程的新孤子结构

通过选取另一类种子解，给出了(2+1)维非线性KdV方程的一类变量分离新解.适当地选择变量分离新解中的任意函数和条件函数，揭示了一类新型孤子结构，如周期性孤波结构、环状孤子结构、曲线型孤子结构等.可以发现(2+1)维非线性KdV方程存在的这类新型孤子结构，是无法通过以往文献中给出的通用变量分离表达式得到的，而且这类新型孤子结构对于实际自然现象的解释有积极的意义. 关键词： 变量分离法 (2+1)维非线性KdV方程 新孤子结构     

色散控制光孤子系统性能分析

研究色散控制光孤子系统中的放大器的自发辐射噪声与交叉相位调制对孤子传输特性的影响，采用变分法分析了色散控制孤子的均方频移、定时抖动和误码特性，从降低自发辐射噪声和交叉相位调制扰动引起的均方频移出发，确定了补偿段的特性参量，给出了三种传输控制方案，分析了各方案中色散控制孤子的传输特性，其结果对色散控制孤子系统的设计具有参考价值。     

两个非线性发展方程的双向孤波解与孤子解

采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解. 关键词： 齐次平衡法 孤子解 孤波解 广义Boussinesq方程 bidirectional Kaup-Kupershmi dt方程     

高阶非线性薛定谔方程的精确周期解和孤波解

本文利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶非线性薛定谔方程,得到了它的包络型Jacobian椭圆函数双周期解和孤波解.分析结果表明亮孤子的存在依赖于负三阶色散效应,暗孤子的存在依赖于正三阶色散效应.     

Numerical investigation of soliton molecules with variable separation in passively mode-locked fiber lasers

Soliton molecules evolution is numerically investigated in a passively mode-locked fiber laser based on the nonlinear polarization rotation (NPR) technique. Peak-to-peak separation of soliton molecules can be controlled by changing either pump strength or cavity linear phase delay appropriately. Moreover, soliton molecules with intensity-independent evolution, separation-independent evolution and large intensity-vibrating evolution are numerically found, respectively. The characteristics of soliton molecules evolution versus linear phase delay or pump strength are given. Periodic stable evolution regimes are found. The separation-controllable soliton molecules can be attributed to the mutual effects of phase delay, Kerr nonlinearity and other parameters of the cavity.     

Chaotic dynamics of a passively mode-locked soliton fiber ring laser

We report on the experimental and numerical studies of the chaotic dynamics of a soliton fiber ring laser passively mode-locked by using the nonlinear polarization rotation (NPR) technique. Period-doubling route to chaos on the soliton repetition rate of either the single pulse soliton or the bound solitons of the laser was experimentally observed. Based on a coupled complex Ginzburg-Landau equation model and also taking into account the laser cavity effect, we further show numerically that the period-doubling bifurcations and route to chaos are intrinsic properties of the laser, whose appearance is independent of the details of the laser cavity design and the laser soliton operation. Property of the solitons under the dynamical bifurcations is also numerically investigated.     

L-band polarization-controlled multiple dissipative solitons generation in a normal dispersion fiber ring laser

A polarization-controlled multiple dissipative solitons generation in a normal dispersion fiber ring laser operating in L-band is demonstrated. The fiber laser is passively mode-locked with nonlinear polarization rotation (NPR) technique. Depending on the rotations of the PCs, the number of the pulses circulating in the laser cavity can be tuned from 1 to 4. The experimental results suggest that the generation of multiple pulses is caused by the soliton shaping of dispersive waves induced by the variations of spectral filtering effect.     

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.     

Thermodynamic properties of the SU(2)f chiral quark–loop soliton

We consider a chiral one-loop hedgehog soliton of the bosonized SU(2)_f Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent quarks. Energy and radius of the soliton are determined in self-consistent mean-field approximation. Quasi-classical corrections to the soliton energy are derived by means of the pushing and cranking approaches. The corresponding inertial parameters are evaluated. It is shown that the inertial mass is equivalent to the total internal energy of the soliton. Corrected nucleon and δ isobar masses are calculated in dependence on temperature and density of the medium. As a result of the self-consistently determined internal structure of the soliton the scaling between constituent quark mass, soliton mass and radius is noticeably disturbed. Received: 26 September 1997     

(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 Series of Variable Separation Solutions and New Soliton Structures of (2+1)-Dimensional Korteweg-de Vries Equation

Variable separation approach is introduced to solve the (2 1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.     

A Series of Variable Separation Solutions and New Soliton Structures of （2＋1）-Dimensional Korteweg-de Vries Equation

Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model （24）. Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.     

Soliton Perturbations of the Modified Korteweg de Vries Equation

The soliton perturbations of the modified Korteweg de Vries equation corresponding to different signs of the nonlinear term are studied. The first-order effects of perturbation on a soliton, namely, both the slow time-dependence of the soliton parameters and first-order corrections are derived in a direct approach based on the separation of variables.     

Lump and Stripe Soliton Solutions to the Generalized Nizhnik-Novikov-Veselov Equation

With the aid of the truncated Painlevé expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters.