非线性演化方程的孤立波解

用齐次平衡原则和辅助微分方程方法得到了6个重要的n次非线性演化方程的孤立波解.辅助微分方程方法的主要思想是借助简单的可解微分方程的解去构造复杂的非线性演化方程的行进波解.这里简单的可解微分方程称为辅助微分方程.本文使用的辅助方程有双曲正割幂型解或双曲正切幂型解.     

Propagation of optical beams in strongly nonlocal nonlinear media

The propagation of arbitrary laser beams in strongly nonlocal nonlinear media is investigated based on the ABCD matrix. The second-order moment beam width and the mean curvature radius are derived under the off-waist incident condition.     

Prediction of the two-tone suppression and intermodulation performance of auditory systems

Using a model based on subcritical Hopf amplifiers, closed form expressions are obtained for two-tone suppression and the third-order intermodulation performance of the human auditory system. The proposed model approximates the Hopf amplifier characteristic using Fourier-series expansion. The parameters of the Fourier-series approximation can be easily obtained without recourse to sophisticated curve-fitting techniques. The results are compared with previously reported observations.     

Harmonics of Tollmien — Schlichting waves in a compressible boundary layer

The harmonics of Tollmien—Schlichting waves in a compressible boundary layer of a plate are computed with the aid of nonlinear parabolized stability equations. At the (downstream) growth of the second harmonic amplitude up to the values of the order of the basic harmonic amplitude, the amplification rate of the latter is shown to increase abruptly. A similar rapid deviation from the results of the linear theory characterizes the onset of the boundary-layer transition to turbulent state. Computations are carried out for the Mach numbers M = 0.01 and 2. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-01-00079a).     

饱和非线性光学介质中的变折射率光学工程

文章概述了在饱和非线性介质中的变折射率光学工程的主要目的、内容和记录方式的类型，展示了国内外的发展动态及目前存在的主要问题，并提出了相应的解决办法。对应于不同的信号光强与背景光强之比，作者提出了可以进行“梯度型”和“阶跃型”变折射率元以及器件的记录和制作的新思路。在光生伏打光折变介质中，针对极低的暗辐照导致很长的记录时间以及介质的各向异性引起二维变折射率元、器件的畸变等问题，可以采用非相干均匀辐照光束来解决。     

Buckling and post-buckling of piezoelectric plates using finite element method

The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mechanics. Buckling and post-buckling of piezoelectric-plate with various boundary conditions are investigated. The calculated results show that piezoelectric effects and external voltage can hardly affect the buckling and post-buckling characteristics of piezoelectric-plate under uniaxial pressure while the buckling caused by displacement in-plane has much to do with the electric field. The present work is supported by the National Natural Science Foundation of China (No. 59635140).     

Nonlinear optical media in photonic crystal waveguides: Intrinsic localized modes and device applications

A review is given of some of the properties of photonic crystal waveguides containing or interacting with nonlinear optical media including discussions of potential device applications. An introduction is given to photonic crystals, photonic crystal waveguide technologies, the properties of Kerr nonlinear dielectric media, the properties of new types of excitations in these systems known as intrinsic localized modes, and optical bistability. Device designs for switches, waveguide couplers, interferometers, transistors, photonic crystal receivers and transmitters, and photonic crystal sensors are reviewed. © 2007 Wiley Periodicals, Inc. Complexity 12: 18–32, 2007     

Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity

This paper addresses chaos anti-synchronization of uncertain unified chaotic systems with dead-zone input nonlinearity. Using the sliding mode control technique and Lyapunov stability theory, a proportional–integral (PI) switching surface is proposed to ensure the stability of the closed-loop error system in sliding mode. Then a sliding mode controller (SMC) is proposed to guarantee the hitting of the switching surface even with uncertainties and the control input containing dead-zone nonlinearity. Some simulation results are included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.     

Propagation of Gaussian wave packets in thin periodic quantum waveguides with a nonlocal nonlinearity

We consider the nonlinear Schrödinger equation with an integral Hartree-type nonlinearity in a thin quantum waveguide and study the propagation of Gaussian wave packets localized in the spatial variables. In the case of periodically varying waveguide walls, we establish the relation between the behavior of wave packets and the spectral properties of the auxiliary periodic problem for the one-dimensional Schrödinger equation. We show that for a positive value of the nonlinearity parameter, the integral nonlinearity prevents the packet from spreading as it propagates. In addition, we find situations such that the packet is strongly focused periodically in time and space.     

光子晶体的制备方法及其应用

光子晶体是一种介电常数不同的、其空间呈周期分布的新型光学材料。由于光子晶体具有光子带隙、光子局域和控制光子态密度等特性,所以它具有广阔的应用前景。简述了光子晶体的主要特征,重点介绍了其制备方法、进展以及实际的和潜在的应用。