Instability of Solitary Waves in Nonlinear Composite Media

In this paper,we investigate a class of Hamiltonian systems arising in nonlinear composite media.By detailed analysis and computation we obtain a decaying estimates on the semigroup and prove the orbitalinstability of two families of explicit solitary wave solutions (slow family in anisotropic case and solitary wavesin isotropic case),which theoretically verify the related guess and numerical results.     

具非线性中立项的二阶时滞微分方程的振动性质

By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.     

Fast Optical Switching Using Oriented Cyanine Dye-Doped Nematic Liquid Crystal

A cyanine dye, 2-[7-（1,3-dihydro-1,3,3-trimethyl-2H-indol-2-ylidene）-1,3,5-heptatrienyl]-1,3,3-trimethyl-3H-indolium iodide （NK-125）, is doped in 4-cyano-4＇-pentylbiphenyl （5 CB）, and the mixture is sandwiched between two pieces of rubbed glass plates. The third-order nonlinear optical properties of the oriented NK-125-SCB layers are measured by the resonant femtosecond degenerate four-wave mixing （DFWM） technique at 760 nm. The third-order nonlinear optical susceptibility of one of the present samples is 5.5×10^-8 esu. The slow DFWM response of the NK-125-SCB layers due to a population grating is accelerated by the increasing laser power because of amplified spontaneous emission （ASE）. On the other hand, we do not observe a similar phenomenon for NK-125- polyethylene glycol （PEG-400）. Oriented NK-125 molecules in nematic liquid crystals must have very high ASE efficiency. Hence the population grating in a DFWM signal disappears within about 4 ps. It is expected that NK-125-SCB can be used as a material for very fast all-optical switching.     

年龄相关的非线性时变种群扩散系统最优分布控制的存在性

讨论了一类非线性时变种群扩散系统的最优分布控制问题,利用LionsJL的偏微控制理论和先验估计,证明了系统最优分布控制的存在性.所得结果可为非线性种群扩散系统中的最优控制问题的实际研究提供必要的理论基础.     

High-Dimensional Nonlinear Envelope Equations and Nonlinear Localized Excitations in Photonic Crystals

We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and long-wavelength mean fields, generated by the self-interaction of the wave packet, are governed by a set of coupled high-dimenslonal nonlinear envelope equations, which can be reduced to Davey-Stewartson equations and thus support dromionlike high-dimensional nonlinear excitations in the system.     

单调和Fuzzy单调变分不等式的补偿方法

在实自反Banach空间,用补偿方法研究单调和Fuzzy单调广义非线性变分不等式,得到了几个解的存在性定理.改进和推广了Browder,Pascali-Sburlan,Zhang等人的各种结果.     

Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems

We consider several synchronous and asynchronous multisplitting iteration schemes for solving aclass of nonlinear complementarity problems with the system matrix being an H-matrix.We establish theconvergence theorems for the schemes.The numerical experiments show that the schemes are efficient forsolving the class of nonlinear complementarity problems.     

一类死区非线性输入系统的自适应模糊控制

针对一类具有死区非线性输入的非线性系统,基于滑模控制的基本原理,利用II型模糊逻辑系统对未知函数进行在线逼近,提出了一种具有监督器的自适应模糊滑模控制方法。该方法通过监督控制器保证闭环系统所有信号有界,并通过引入最优逼近误差的自适应补偿项来消除建模误差的影响。通过理论分析,证明了跟踪误差收敛到零。     

Excitation Properties of the Biological Neurons with Side-Inhibition Mechanism in Small-World Networks

We have studied the excitation properties of biophysical Hodgkin-Huxley neurons with the side-inhibition mechanism in small-world networks. The result shows that the excitation properties in the networks are preferably consistent with the characteristic properties of a brain neural system under external constant stimuli, such as fatigue effect, extreme excitation principle, and the brain neural excitation response induced by different in- tensity of noise and coupling. The results of the study might shed some light on the study of the brain nerve electrophysiology and epistemological science.     

Bistable Behaviour of N Two-Level Atoms Interacting with the Field inside a High-Q Cavity Containing a Nonlinear Kerr-Like Medium

Taking the intensity-dependent coupling between atoms and cavity mode into account, we investigate a system consisting of N homogeneously broadened two-level atoms interacting with the field inside a single-mode Fabry- Perot cavity containing a nonlinear Kerr-like medium. We derive the steady-state bistable behaviour of the system, and further analyse in details the influence of several critical parameters on the bistable behaviour.