Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation

Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.     

基于热致非线性效应的暗空间光孤子实验研究

实验研究了热致非线性效应作用下，Ｃ＾６０甲苯溶液中强连续激光激发暗空间光孤子的过程，并给出了数值模拟结果。     

向列相液晶中强非局域空间光孤子的实验观察

通过实验对向列相液晶中的非局域空间光孤子的传输进行了研究。理论上基于非线性的液晶孤子传输方程,采用高斯形式的试探解,得到了孤子传输的解析解,以及对液晶中的非局域孤子和Snyder等提出的强非局域孤子模型的结果进行了比较。实验上,观察了空间光孤子在向列相液晶中的传输,找到了不同束宽下空间光孤子的临界功率。比如束宽为2μm时临界功率为2.0mW。观察了向列相液晶中空间光孤子的弛豫过程,并注意到液晶分子的响应时间长达几秒钟,液晶中的孤子形成速度较慢。     

Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation

Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.     

Nonlinear All-Optical Switching Device by Using the Spatial Soliton Collision

We propose a new nonlinear all-optical switching device by using the spatial solitons collision. This is 1 × N switching device controlled by two control beams. The numerical results show that this device could really function as a 1 × N all-optical switching device. This device is a potential key component in the application of optical signal processing and optical computing systems.     

Nonlinear All-Optical Switching Device by Using the Spatial Soliton Collision

We propose a new nonlinear all-optical switching device by using the spatial solitons collision. This is 1 × N switching device controlled by two control beams. The numerical results show that this device could really function as a 1 × N all-optical switching device. This device is a potential key component in the application of optical signal processing and optical computing systems.     

梯度折射率非局域介质中空间孤子振荡行为研究

应用等效粒子近似方法研究了光学空间孤子在带有局域和非局域非线性横向非均匀介质中的传输动力学行为.发现孤子在传播过程中横向的周期性振荡.折射率调制幅度和波导的归一化宽度决定了振荡周期的大小.介质的非局域对振荡振幅有着较小的影响.模拟了孤子传输过程,所得数值结果与理论分析符合很好.此外,模拟传输还发现多孤子束缚态能够在这个模型中稳定传播.这种振荡特性或许可以应用于光学路由器、转换器、开关等.     

波前扰动产生空间暗光孤子及孤子演化的实验研究

报道实验上观测到用波前扰动的空间光暗孤子的产生及演化规律，实验测量表明，首先，产生的空间暗孤子的空间轮廓是双曲正割型的函数，这与逆散射理论上的空间暗孤子解是一致的其次，观测了空间暗光孤子在自散焦介质中的演化过程，实验结果与非线性薛定谔方程计算机数值模拟的结果是一致的，结果表明，空间暗光子随着光束传输过程逐渐演化并在演化过程中逐渐形成了多个孤子对；最后，测量了不同细丝宽度，非线性系数与光强子空间暗孤     

CTE Solvability,Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System

A consistent tanh expansion (CTE) method is used to study the modified Boussinesq equation. It is proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by the Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependent variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initial value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among solitons and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wave interaction behaviors are studied both in analytical and graphical ways.     

Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev-Petviashvili Equation

A generalized Kadomtsev-Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev-Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev-Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.     

All-optical Steerable Directional Coupler Using Kerr Dark Spatial Soliton Waveguides

1.IntroductionOpticalspatialsolitoninduced-waveguidesareofgreatresearchinterestrecently[1-8]becauseoftheirPOtentialapplicationinopticalcommunicationsandopticalcompution.Asoliton--inducedwaveguidecanguidelightinself--focusingorself--defocusingKerr-typemediabecausethesolitonbeaminducesarefractive-indexprofileequivalenttoanordinarydielectricwaveguide.Soliton-inducedwaveguidecansupPOrtmanymodesofaprobebeampropagatingcoaxiallyalongthesolitonwaveguideSoliton-inducedwaveguideshaveadvantageovertheir…     

Nonlocal Symmetry Reductions,CTE Method and Exact Solutions for Higher-Order KdV Equation

The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev′e method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems.The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion(CTE) method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.     

有限高斯背景下空间暗光孤子自诱导波导的模式分析

从有限高斯背景下空间暗光孤子诱导折射率分布出发，用等效衰减矢量法得到它所自诱导的波导的色散特性，并与理想情况的无限背景下空间暗光孤子诱导的色散方程进行了比较。结果表明，当高斯背景越来越宽时，它与无限背景下的结果越来越接近，为在全光器件中实际应用提出了理论依据。     

双光子光折变介质中非相干耦合光伏孤子族

为了得到双光子非相干耦合光伏孤子族的结果,采用数值模拟方法,对稳态情况下多束互不相干的光束在双光子光伏光折变晶体中的传播进行了研究。结果表明:具有相同偏振和相同波长的多束互不相干的入射光束可在晶体中形成双光子非相干耦合光伏孤子族。当入射光束中仅包含两个分量时,孤子族就转化为光伏孤子对。并用双光子光伏光折变晶体Cu:KNSBN和LiNbO3进行了分析说明。研究结果可为空间光孤子理论的发展提供理论依据。     

Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities

Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing χ⁽²⁾ (quadratic) andχ⁽³⁾ (cubic) nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.     

基于强非局域空间光孤子的温度传感器原理

为了让温度传感器在集成化全光控制中找到实现途径,提出一种基于非局域空间光孤子传输的温度传感器的理论方案.以铅玻璃作为非局域空间光孤子的传输介质,通过研究圆柱形铅玻璃中, 中心入射光束在传输过程中的相移问题, 得出在环境温度0.32 ℃的改变就可以引起孤子π相移的结论.此温度改变对相移的调制有望为基于干涉仪原理的温度传感器提供一个可行且灵敏度较高的实现方案.     

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.     

P(o)schl-Teller势阱中非局域效应对透射光谱的影响

在考虑半导体量子阱中导带电子对外加激光场非局域光学响应的情况下,利用格林函数方法推导出了光透射率的解析表达式,并以典型的GaAs/AlGaAs为材料的P(o)schl-Teller量子势阱为例进行数值计算.计算结果表明,由于电子对激光场的非局域光学响应,半导体量子阱的透射光谱的谱线在共振峰附近出现明显地蓝移,蓝移的大小与量子阱宽度有紧密的联系.在有效的纳米尺度范围内,半导体量子阱越宽,透射谱线的蓝移也就越大.另外,光场强度和量子阱结构参数等因素对透射光谱的影响也被澄清.     

Soliton Propagation in Optical Fibers with Random Polarization Dispersion

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Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation

Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries (ABmKdV) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-mKdV equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events".