基于二维广义非线性薛定谔方程的逆级联现象

在外部势场和初始空间局部有限振幅脉冲给定的情况下,基于二维广义非线性薛定谔方程i?_tE+p▽²E+[V(x,y)+q|E|²]E=0,研究了波的不稳定性随时间的演化。波的不稳定性演化主要依赖于方程里的群色散系数p=p_r+ip_i和非线性系数q=q_r+iq_i,数值结果发现系统会出现调制不稳定性、波坍缩、逆级联以及整个空间的湍流态。当p=3.5+0.5i,q=8.0+0.9i时,数值结果发现系统在出现部分逆级联之后波场的能量主要聚集在波矢量k空间中半径|k|≥100的短波区域,同时形成了以区域中心为圆心,半径|k|≈100的圆形相对稳定区域。当粘性阻尼系数p_i在[0.1,1.0]时,数值结果发现产生逆级联的部分区域随着p_i(<1.1)的不断增大而逐渐缩小,相对稳定的圆域半径从零开始逐渐增大。因此,粘性系数p_i相当于系统中的一个调节开关,调整它在一定范围(p_i<...     

五阶克尔非线性光纤放大器中光脉冲的传输特性

以变系数高阶非线性薛定谔方程为理论模型,对光脉冲在具有五阶非线性克尔效应光纤放大器中的传输特性进行了研究.在加入振幅微扰、相位扰动、噪声微扰的情况下,数值模拟了亮孤波、灰孤波和黑孤波在光纤系统中的传输稳定性,并且讨论了孤子间的相互作用.数值模拟结果表明:在有限的微扰下,三种光脉冲具有良好的传输稳定性.     

用推广的李群约化法求解非线性薛定谔方程

用推广的经典李群约化法，得到了色散系数、非线性系数、补偿（或损失）系数为时、空变量函数时的非线性薛定谔方程的精确解.深入研究了非线性薛定谔模型的一般孤波解与线性调频孤波解在光纤通讯与光纤放大器中的潜在应用. 关键词： 李群约化 非线性薛定谔方程 光纤通讯     

非均匀掺铒光纤中的可控呼吸子与多峰孤子

研究了耦合广义非均匀非线性薛定谔-麦克斯韦-布洛赫方程所描述的非均匀掺铒光纤系统中不同非线性局域波的色散与非线性管理问题.利用相似变换求解非均匀非线性薛定谔-麦克斯韦-布洛赫方程,得到一个非自治的通解形式.该解在非均匀掺铒光纤系统中包含了众多的非线性局域波结构.从非线性局域波的复现与相移非线性局域波考虑,在色散与非线性管理系统下分析了呼吸子和多峰孤子的动力学特性.结果表明在非均匀掺铒光纤系统中存在新的非线性局域波结构,并且在色散与非线性管理系统下非线性局域波的结构呈现多样性,这对实际的光纤通信理论有参考意义.     

非线性薛定谔方程数值解法中傅立叶正逆变换选取的讨论

讨论了光波场正负频表示与正逆傅立叶变换形式的选取及非线性薛定谔方程的形式密切相关，指出了现在熟知的非线性薛定谔方程形式是选取负频表示的结果，因此正逆傅立叶变换形式的选取就不是任意的．在采用基于傅立叶变换数值方法解非线性薛定谔方程时，要注意所用编程语言中快速傅立叶变换正逆变换的形式．而在大多数编程语言中其快速傅立叶变换正逆变换形式是与非线性光学中应采用的傅立叶变换正逆形式恰好相反，因此时而出现一些错误的计算结果．分析了这些错误的原因，并给出了正确结果。     

二维梯度折射率光波导中线光畸形波的传播控制

非均匀非线性波导中光脉冲的传播由(2+1)维变系数非线性薛定谔方程描述。采用相似变换方法求解了(2+1)维变系数非线性薛定谔方程的精确畸形波解,并讨论了带有外势项的非线性薛定谔方程控制的线光畸形波在波导放大器中的传播问题。给出了操控线光学畸形波解传播的控制条件,发现线光畸形波的特性,如振幅和位置等,在非线性光学介质中是可以控制的。在可控参数条件下,讨论了可控光畸形波在非线性介质中的传播行为,包括延迟激发、抑制和保持。研究结果在理论和实际应用上都具有重要意义。     

非线性系数对超晶格透射的影响

研究了非线性系数对超晶格中波透射的影响.把非线性薛定谔方程转化成二阶差分方程，通过迭代此差分方程得到透射谱.透射谱显示非线性系数对波的透射有明显的调制作用. 关键词： 透射 非线性Kronig-Penny模型 非线性系数     

生长及耗散波色-爱因斯坦凝聚中的怪波

利用达布变换法(Darboux transformation),解析的研究了生长及耗散波色-爱因斯坦凝聚(BEC)中的怪波.通过降维和无量纲化,将描述BEC的Gross-Pitaevskii (GP)方程转化成一维无量纲非线性薛定谔方程.利用达布变换,得到了一维非线性薛定谔方程的怪波解析解.根据解析结果,数值模拟了生长及耗散BEC中怪波的性质.结果表明,BEC中出现了一种典型的双洞怪波,并且BEC生长会延缓怪波的消失,而BEC的耗散会加速怪波的消失.     

形变相干光场与级联型三能级原子相互作用中场的反聚束效应

建立了q形变光场与级联型三能级原子相互作用的非线性理论, 求得相互作用绘景中薛定谔方程的形式解及在其态下的期望值, 利用数值计算揭示了q形变对场与三能级原子相互作用中场反聚束效应的影响. 研究发现q偏离1的程度越大, q形变对场反聚束效应的调控能力越强, 反映出q形变的非线性行为对量子相干性的干扰以及对量子特性的影响. 当q→1时, 恢复为普通线性理论.     

光子晶体光纤超连续谱的孤子俘获数值研究

通过数值求解广义非线性薛定谔方程, 本文对光子晶体光纤中超连续谱的孤子俘获现象进行研究. 利用交叉相关频率分辨光学开关(X-FROG)技术, 观测并记录了超连续谱沿着光纤长度的演化, 得到孤子俘获的整个过程. 研究发现: 当满足相位匹配条件时, 孤子与非孤子辐射波发生四波混频, 产生的俘获波频谱随着孤子红移而逐渐蓝移; 增加抽运功率, 孤子与俘获波的作用增强. 为可调谐超短脉冲和超连续谱研究提供理论依据.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion accoustic waves in a dust plasma with ion-dust collision effects is studied.Using the perturbation method,a modified nonlinear Schroedinger equation contains a damping term that comes from the effect of the ion-dust collision is derived.It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Rapid beat generation of large-scale zonal flows by drift waves: a nonlinear generic paradigm

The generalized Charney-Hasegawa-Mima equation is unstable to a four wave modulational instability whereby a coherent, monochromatic drift wave can drive a band of modes and associated zonal flows unstable. Although initially the fastest growing modes dominate, a secondary nonlinear instability later drives the longest wavelength zonal flow and its associated sidebands at twice the growth rate of the fastest growing modulationally unstable modes. This results in a direct transfer from strongly unstable short wavelength modes to the weakly unstable long wavelength modes, which drains the short wavelength pump energy. A related but less efficient direct enstrophy cascade generates very short wavelength modes lying outside the band of modulationally unstable modes.     

Modulated Dust-Acoustic Wave Packets in an Opposite Polarity Dusty Plasma System

The nonlinear propagation of the dust-acoustic bright and dark envelope solitons in an opposite polarity dusty plasma(OPDP) system(composed of non-extensive q-distributed electrons, iso-thermal ions, and positively as well as negatively charged warm dust) has been theoretically investigated. The reductive perturbation method(which is valid for a small, but finite amplitude limit) is employed to derive the nonlinear Schr¨odinger equation. Two types of modes, namely, fast and slow dust-acoustic(DA) modes, have been observed. The conditions for the modulational instability(MI) and its growth rate in the unstable regime of the DA waves are significantly modified by the effects of non-extensive electrons, dust mass, and temperatures of different plasma species, etc. The implications of the obtained results from our current investigation in space and laboratory OPDP medium are briefly discussed.     

Dissipation of Nonlinear Wave in Inhomogeneous Dust Plasma Crystal

A Korteweg-de Vires-type (KdV-type) equation and a modifiedNonlinear Schrödinger equation (NLSE) for the dust lattice wave(DLW) are derived in a weakly inhomogeneous dust plasma crystal. Itseems that the amplitude and the velocity of the dust lattice solitary waves decay exponentially with increasing time in a dust lattice. The modulational instability of this dust lattice envelope waves is investigated as well. It is found that the waves are modulational stable under certain conditions. On the other hand, the waves are modulational unstable if the conditions are not satisfied.     

Kuznetsov–Ma soliton and Akhmediev breather of higher-order nonlinear Schrdinger equation

In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schrdinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability(MI) process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov–Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schrdinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton's peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses.     

Spatial quantum noise in singly resonant second-harmonic generation

We study the spatial distribution of quantum noise in singly resonant second-harmonic generation. Calculations are performed below threshold for spatial modulational instability. For parameters for which the intracavity fields are modulationally stable the spatial spectrum shows maximum squeezing at k=0, whereas under conditions of modulational instability we find maximum squeezing at finite wave number |k|=k(c), where k(c) corresponds to the classical critical wave number.     

二维玻色-爱因斯坦凝聚中孤立波的调制不稳定性

研究了盘状势阱中二维玻色-爱因斯坦凝聚(BEC)的孤立波. 在平均场理论下, 由BEC所满足的Gross-Pitaevkii方程出发导出了二维BEC所满足的非线性Schrödinger方程. 从该方程出发, 研究单组分常振幅二维BEC(单组分常振幅 BEC)的调制不稳定性, 得到了该系统相应的增长率. 关键词： 孤子 不稳定性 玻色-爱因斯坦凝聚     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

Discrete nonlinear Schrödinger equation with arbitrary nonlocality: Linear stability analysis and localized solution

The modulational instability of a plane wave for a discrete nonlinear Schrödinger equation with arbitrary nonlocality is analyzed. This model describes light propagation in a thin film planar waveguide arrays of nematic liquid crystals subjected to a periodic transverse modulation by a low frequency electric field. It is shown that nonlocality can both suppress and promote the growth rate and bandwidth of instability, depending on the type of a response function of a discrete medium. A solitary wave (breather-like) solution is built by the variational approximation and its stability is demonstrated.