Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field

The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.     

一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=     

一类催化反应中的非线性奇摄动边值问题的渐近解

本文研究了催化反应非线性奇摄动边值问题．利用微分不等式理论和方法，得到了问题的解的任意次近似渐近估计．     

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

Ti(IV)/BINOL-catalyzed asymmetric aldol reaction of a masked acetoacetic ester: pronounced influence of catalyst concentration on nonlinear effects

Initial concentration of enantioenriched or enantiopure catalysts proved to be an important factor for the achievement of a more pronounced amplification of ee's in the Ti(IV)/BINOL-catalyzed aldol reaction of an O-silyldienolate.     

厚高阶光学非线性介质Z扫描的变分法分析

利用变分法对具有五阶光学非线性介质的Z扫描特性进行了研究。通过比较，发现当介质在具有较大的五阶非线性系数或较大光强的情况下，五阶非线性项的作用是不可忽略的。这对光限制器的设计和Z扫描实验都具有一定的指导意义。     

Phase and Amplitude Characteristics of Injection Lasers with Allowance for the Effects of Nonlinear Amplification in Current Modulation

The influence of the parameter of amplitude-phase coupling for nonlinear amplification on the phase-frequency characteristics of an injection laser in the regime of pumping current modulation has been investigated theoretically. The parameter is defined as the coefficient of proportionality between changes in the real and imaginary parts of the refractive index during variation of the density of photons in the cavity. The substantial dependence of the coefficient of phase modulation on the parameter of the amplitude-phase coupling for nonlinear amplification at small modulation frequencies is shown. A technique to determine the indicated parameter based on the frequency dependence of the ratio between the coefficients of phase and amplitude modulation is suggested.     

Self-Diffraction of Bessel Light Beams in a Nonlinear Medium

The phenomenon of self-diffraction of Bessel light beams (BLB) in a nonlinear liquid medium has been studied experimentally and theoretically for the first time. Diffraction maxima which do not correspond to integer orders for an induced periodic structure have been registered. It has been shown that the appearance of these maxima is due to the initial BLB modulation, which can be caused by the departure of the axicon refracting surface from the ideal conical surface, as well as by the imperfection of the form of the Gaussian beam incident on the axicon.     

一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

用数值方法分析微孔激光器出射光的近场特性

微孔激光器作为应用于近场光信息存储系统中的一种新型光源，它的出射光斑的近场特性对于近场光存储是十分重要的。针对纳米孔径运用角谱进行Fox-Li数值迭代，得到不同孔径微孔激光器的基模光强分布，然后运用二维非线性时域有限差分法分析微孔激光器出射端即微孔金属膜的近场光学性质，模拟计算了不同孔径和厚度的微孔金属膜的光强近场分布，从应用于近场光存储的角度，给出反映其近场光学特性的相关数据。发现由于TM模式下金属存在局域表面等离子增强效应，使得其出射强度比TE模式高一个数量级，从而更适于作为实际中近场光存储系统和原理试验的光学头。