具微结构地壳中非线性地震波的演化

非线性地震波在地壳中传播及演化规律的研究具有重要实际意义.利用有限差分方法, 对非线性地震纵波和横波在具微结构地壳中的演化过程进行了详细的数值模拟.结果表明,非线性地震纵波和横波在具微结构地壳中可以逐渐演化成一个孤立波或两个孤立波或孤立波列或消失.地震波的初始幅度、频散系数和体力因子对演化过程和结果都有重要影响.研究结果揭示了非线性地震波在一种微结构地壳中的演化规律,这有助于在理论上解释一些特殊地震波现象.     

非线性Schroedinger方程的动力学行为分析

采用辛算法数值求解非线性Schroedinger方程的周期初值问题，建立不同的相空间来分忻其动力学持性．首先比较分析了不同的相空间中立方非线性Sehroedinger方程在不同立方非线性参数下的长时间演化的动力学特性，然后讨论了相空间中立方一五次方非线性Sehroedinger方程在不同立方和五次方非线性参数下的长时间演化的动力学特性，数值结果显示，对于不同的立方非线性参数，随着五次方非线性参数的增加，动力学行为的演化路径是不一样的．     

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     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,拓展非线性振动教学内容.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

非线性Kronig-Penney超晶格的二维实映射分析

通过二维实映射研究非线性Kronig-Penney超晶格中的波输运特性，数值计算得到波矢一定情况下不同非线性系数的映射图、以及非线性系数一定情况下不同波矢的映射图.非线性Kronig-Penney超晶格中的非线性，对超晶格中波函数的Bloch波矢有明显的调节作用.随着非线性系数的增大，映射图由周期函数的有限个分立点变为准周期函数的一条闭合轨道、以及有规则或无规则的点分布. 关键词： 非线性Kronig-Penney超晶格 非线性效应 二维实映射 波矢     

一类非线性演化方程的新多级准确解

在Lamé方程和新的Lamé函数的基础上，应用小扰动方法和Jacobi椭圆函数展开法求解一类非线性演化方程（如mKdV方程，非线性Klein-Gordon方程Ⅱ等），获得多种新的多级准确解 .这些多级准确解对应着不同形式的周期波解.这些解在极限条件下可以退化为多种形式的孤 立波解，如带状孤立子、钟形孤立子等. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法     

空频复用光纤中四波混频过程的解析分析方法

空分复用(SDM)与波分复用(WDM)的结合有效提升了光纤通信系统的容量,其中光纤的非线性影响不可忽视.本文将光纤四波混频作用过程由WDM频域推广到模分复用(MDM)空间域,第一次给出抽运消耗情形下空频域四波混频的统一解析表达式.通过数值计算非简并四波混频耦合模方程的幅度和相位演化特性,验证了解析分析方法的正确性.讨论了解析解在多波耦合方程简化、大规模并行相位运算器设计以及快速非线性补偿等方面的应用.     

考虑频散效应的一维非线性地震波数值模拟

非线性理论是解决地学问题的重要手段, 充分认识非线性波动特征有助于解释实际观测资料中的一些特殊地震现象. 本文基于Hokstad改造的非线性本构方程, 利用交错网格有限差分法实现了固体介质中一维非线性地震波数值模拟; 采用通量校正传输方法消除非线性数值模拟中波形振荡, 提高模拟精度. 通过与解析解的对比验证了模拟结果的正确性. 研究结果显示了非线性系数对地震波的传播有重要影响, 并且当取适当的非线性和频散系数时, 地震波表现出孤立波的传播特性. 最后分析了不同的非线性地震波在固体介质中的传播演化特征.     

飞秒光孤立波解传输的稳定性分析

针对高阶非线性薛定谔方程任意参量下的飞秒光孤立波解，用数值演化方法考察了该光脉冲在受到各种初始扰动时的稳定性。结果表明：当飞秒光脉冲受到振幅及波形扰动时可以稳定传输，对于随机噪声及啁啾的扰动，在一定范围内也可传输，这有可能为进一步实现飞秒光脉冲在光纤中的无畸变传输提供一定的理论依据。     

On the amplification of wind nonlinear waves due to the vortex formation in separated flow

A hypothesis about the intensification of waves by the air vortices formed on the leeward side of the wave is proposed. It is assumed that the vortices attract the water surface, thus increasing the wave amplitude. The hypothesis is verified using experimental data for nonlinear waves.     

Post-solitons and electron vortices generated by femtosecond intense laser interacting with uniform near-critical-density plasmas

Generation of nonlinear structures, such as stimulated Raman side scattering waves, post-solitons and electron vortices, during ultra-short intense laser pulse transportation in near-critical-density (NCD) plasmas is studied by using multi-dimensional particle-in-cell (PIC) simulations. In two-dimensional geometries, both P- and S-polarized laser pulses are used to drive these nonlinear structures and to check the polarization effects on them. In the S-polarized case, the scattered waves can be captured by surrounding plasmas leading to the generation of post-solitons, while the main pulse excites convective electric currents leading to the formation of electron vortices through Kelvin-Helmholtz instability (KHI). In the P-polarized case, the scattered waves dissipate their energy by heating surrounding plasmas. Electron vortices are excited due to the hosing instability of the drive laser. These polarization dependent physical processes are reproduced in two different planes perpendicular to the laser propagation direction in three-dimensional simulation with linearly polarized laser driver. The current work provides inspiration for future experiments of laser-NCD plasma interactions.     

Competition between traveling fluid waves of left and right spiral vortices and their different amplitude combinations

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counterrotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude-equation approximations. Stable cross-spiral structures with continuously varying content of left- and right-spiral modes are found. They provide a stability transferring connection between the initially stable, axially counterpropagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly farther away from the onset of vortex flow.     

On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation

The nonlinear Schr?dinger equation (NLS) has been a fundamental model for understanding vortex motion in superfluids. The vortex motion law has been formally derived on various physical grounds and has been around for almost half a century. We study the nonlinear Schr?dinger equation in the incompressible fluid limit on a bounded domain with Dirichlet or Neumann boundary condition. The initial condition contains any finite number of degree ± 1 vortices. We prove that the NLS linear momentum weakly converges to a solution of the incompressible Euler equation away from the vortices. If the initial NLS energy is almost minimizing, we show that the vortex motion obeys the classical Kirchhoff law for fluid point vortices. Similar results hold for the entire plane and periodic cases, and a related complex Ginzburg–Landau equation. We treat as well the semi-classical (WKB) limit of NLS in the presence of vortices. In this limit, sound waves propagate through steady vortices. Received: 1 December 1997 / Accepted: 27 June 1998     

Solitary deflection waves on the supersonic domain wall in yttrium orthoferrite

The moving antiferromagnetic vortices are accompanied by solitary deflection waves. These waves allow to investigate generation and nonlinear dynamics of the antiferromagnetic vortices on the moving domain wall with the help of the two- and three-fold digital high speed photography. On the quasi-relativistic domain wall the vortex dynamics is quasi-relativistic with the limiting velocity c=20 km/s, which is equal to the spin-wave velocity. The solitary deflection waves dynamics can be explained assuming existence of the gyroscopic force. A theory for the gyroscopic force in the orthoferrite domain wall is elaborating by A.K. Zvezdin et al. currently. We present a comparison of the theoretical and experimental results on the dynamics of the solitary deflection waves, which accompany the antiferromagnetic vortices in the domain wall of orthoferrites.     

非线性平板光波导中TM波的网络分析

用横向等效网络方法分析了非线性平板波导中TM的色散关系和场分布.这种方法基于传输线理论,把非线性介质波导中复杂的电磁场问题等效于电路网络问题,用横向谐振技术得到色散方程.用数值方法计算了不同非线性机制下三层平板非线性波导中的TM波传输特性.     

Merging of barotropic symmetric vortices. A case study for gulf stream rings

Summary We made numerical experiments to study the merging dynamics of axisymmetric barotropic ringlike vortices using a quasi-geostrophic model in a β-plane. We want to explore the initial conditions and the physical parameters that cause the merging or that affect the merging rates of ringlike structures. The initial vortices have a ?realistic? shape,i.e., they are taken to simulate closely the horizontal structure of Gulf Stream rings. In the first set of experiments we change the initial conditions. The results agree with the classical solution that there is a critical initial separation distanced between the two vortices: for bigger merging distances the process cannot occur. The initial distance affects the merging rates and it determines the development of the lateral arms and the behaviour of the ?near-field? vortices. The latter form near the elongated arms of the merging vortices; sometimes the arms of the merged vortex become unstable and get detached from the central merged vorticity region to form dipolar structures with ?near-field? vortices. A second set of numerical simulations is done by changing the numerical model parameters. The results show that the merging is a nonlinear process very sensitive to the value of the nonlinear parameter, α, and that the β-effect does not alter appreciably the speed of merging but it affects the development of the arms.     

Simulation of viscous flows with undulatory boundaries. Part I: Basic solver

A numerical method for the simulation of viscous flows with undulatory walls and free surfaces is presented. The simulation domain is discretized by a boundary-fitted and time-dependent grid. The Navier–Stokes equations, subject to fully nonlinear kinematic and dynamic boundary conditions at the free surface and no-slip boundary condition at the wall, are simulated by a hybrid pseudo-spectral and finite difference method in space and a semi-implicit fractional-step method in time. The performance of the method is demonstrated by a series of test cases including flows over wavy boundaries, various surface waves, and interaction between vortices and free surfaces. Validation by convergence test and extensive comparisons with previous theoretical, experimental, and numerical studies indicate the accuracy and efficiency of the method. Finally, a simulation example of turbulence and free surface interaction is presented. Results show that the rich features of the free surface such as surface waves, splats, anti-splats, dimples, and scars are captured accurately. Characteristic vortical structures and variation of turbulence statistics in the near-surface region are also elucidated.