广义变系数(3+1)-维非线性薛定谔方程的有限对称群解

基于推广的对称群方法和符号计算,研究了变系数非线性薛定谔方程的有限对称群解。 我们构造了标准的(3+1)-维非线性薛定谔方程和带色散项、非线性项和增益或损耗项的(3+1)-维非线性薛定谔方程的对称变换。 利用该变换,我们从标准的(3+1)-维非线性薛定谔方程中得到了(3+1)-维变系数非线性薛定谔方程丰富的精确解。     

Exact Analytic Solutions for the Caudrey Dodd-Gibbon-Kotera-Sawada Equation

1IntroductionSince the world around us is inherently nonlinear ,nonlinear Partial Differential Equations ( PDEs) arewidely used to describe complex phenomena in variousfields of sciences ,suchas plasma ,fluid dynamics , manyareas of solid state physics ,laser andfiber optics . Vari-ous methods for obtaining explicit traveling solitarywave solutions to nonlinear evolution equations havebeen proposed. Recently,the balancing-act method hasbeen widely applied to derive the nonlinear transforma-t…     

Discrete solitons by the bilinear transformation

A discrete-time sine-Gordon equation is obtained by applying the bilinear transformation to the inverse scattering representation of the sine-Gordon equation. The corresponding discrete soliton solutions and Bäcklund transformations are presented.     

广义变系数KdV-Burgers方程的微分不变量及群分类

应用李无穷小不变规则,得到了广义变系数KdV-Burgers方程的连续等价变换.从等价代数开始,构造了一阶微分不变量并依据微分不变量对方程作了群分类.最后,通过等价变换将一般的变系数KdV-Burgers方程映射为常系数Burgers方程、KdV方程、KdV-Burgers方程.同时,也得到了变系数KdV-Burgers方程的一些精确解.     

A finite-difference time-domain method for solving electromagneticproblems with bandpass-limited sources

The complex-envelope representation of bandpass-limited signals is used to formulate a bandpass-limited vector wave equation and a new finite-difference time-domain (FDTD) scheme that solves the bandpass-limited vector wave equation is presented. For narrow-band electromagnetic systems, this new method allows the time step to be several orders of magnitude larger than current FDTD formulations while maintaining an amplification factor equal to one. Example results obtained by this method are presented and compared with analytic solutions     

An Analytic Model to Account for Quantum–Mechanical Effects of MOSFETs Using a Parabolic Potential Well Approximation

An analytic model to account for the quantum–mechanical effects (QMEs) of the MOSFETs using a parabolic potential well approximation is presented in this paper. Based on the solution of the coupled SchrÖdinger and Poisson equations following the Wentzel–Kramer–Brillouin method, a transcendental equation of the subband energy level has been rigorously derived to obtain an approximate analytic solution for the subband energy levels and the inversion charge centroid. Calculated results from the obtained analytical solution are compared with the previous approximate solutions reported in the literature and the numerically simulated data. A good agreement between the analytical and numerical is obtained, proving the validity of the analytic modeling of QMEs.     

耦合KdV方程的新孤子解

本语文利用函数变换巧妙地将求解偏微分方程组的问题化为求解单个方程问题,得到了耦合ＫｄＶ方程一系列新的孤子新,方法简单明了且具有普遍意义,也可用来解决其它某些类型方程组的求解问题。     

Generalized Zakharov-Kuzentsov方程的类孤子新解

通过两个步骤,构造了Generalized Zakharov-Kuzentsov方程的无穷序列类孤子新解. 第一步、利用首次积分与函数变换,把一种非线性常微分方程转化为几种常用的辅助方程,并获得了几种常用辅助方程的新解、B\"{a}cklund变换和解的非线性叠加公式. 第二步、借助一系列的变换与符号计算系统~Mathematica,构造了Generalized Zakharov-Kuzentsov方程的无穷序列类孤子新解.     

Mismatched linear active 2-ports

A resistively mismatched linear active 2-port can be designed for a given performance factor, so that its power gain is optimum. In this process, a cubic equation has to be solved numerically by hand or machine. Simple and closely accurate analytic solutions for this equation have now been obtained with an error less than 1.5%.     

Analytical Model of Non-dispersion-limited Transient Stimulated Raman Scattering in Single-mode Silica Fiber in WDM Optical Communication System

The non-dispersion-limited analytic solutions of unidirectional N-channel transient stimulated Raman scattering (SRS) coupling wave equation which governing the propagation of the optical signals in single-mode (SM) silica fiber have been presented. Taking into account the SRS cross coupling among the N-channels, the analytic solutions are applicable to the system with arbitrary channel separation and input signal light power.     

广义变系数Burgers-Kadomtsev-Petviashvili方程的自B?cklund变换和精确解析解

应用Painlevé分析法研究了广义变系数Burgers-Kadomtsev-Petviashvili方程。结果显示该方程不具有Painlevé性质。通过截断的Painlevé展开方法，在条件 ( 为任意常数)下, 得到了该方程的自B?cklund变换。基于自B?cklund变换，给出了一些新的解析解如多孤子解和周期解。     

开环位置激励半球谐振陀螺仪工作原理与误差分析

为了研究半球谐振陀螺仪的工作原理,首先推导了谐振子上振动波腹方位角的表达式,然后建立了振动位移和速度的状态方程,进而求出了状态方程的精确解析解,给出了在角速率输入和存在密度分布不均匀缺陷时的波腹方位角的稳态解和角速率解算误差.最后在开环位置激励下,给出了为保证半球谐振陀螺角速率估计精度的密度四次谐波的取值范围.     

首次积分与(n+1)维多重sine-Gordon方程的无穷序列新解

通过几种函数变换把(n+1)维多重sine-Gordon方程的求解转化为常微分方程组的求解.利用常微分方程组的首次积分与可求解几种常微分方程的Bcklund变换和解的非线性叠加公式,构造了(n+1)维多重sine-Gordon方程的无穷序列类孤子新解.     

Multiple-Scale Analysis of Charge Transport in Semiconductor Radiation Detectors: Application to Semi-Insulating CdZnTe

The transport, trapping, and subsequent detrapping of charge in single crystals of semi-insulating cadmium zinc telluride (CdZnTe) has been analyzed using multiple-scale perturbation techniques. This method has the advantage of not only treating impulse charge generation typical in spectroscopic analysis, but also a large class of continuous generation sources more relevant to high-flux x-ray imaging applications. We first demonstrate that the multiple-scale solutions obtained for small-current transients induced by an impulse generation of charge are consistent with well-known exact solutions. Further, we use the multiple-scale solutions to derive an analytic generalization of the Hecht equation that incorporates detrapping over times much longer than the carrier transit time (i.e., delayed signal components). The method is then applied to a continuous charge generation source that approximates that of an x-ray source. The space–time solutions obtained are relevant to detector design in high-flux x-ray imaging applications. Throughout this work the multiple-scale solutions are compared with exact solutions as well as full numerical solutions of the fundamental charge conservation equations.     

Analysis of reduced interband absorption mechanisms insemiconductor quantum wells

Mechanisms for reduced interband absorption using intersubband coherence or intersubband coupling in semiconductor quantum wells are analyzed by exactly solving the density matrix equation. By placing some mild limitations on the diagonal density matrix elements, general analytic solutions are obtained without weak-field restrictions. Our solutions demonstrate reduced absorption, various nonlinear processes, and coupling-field-modulation of interband transitions. Our results agree well with previous results for three-level atomic systems, give insights into nonlinear mechanisms, and point out the importance of nonperturbative approaches to this class of problems     

A treatment of impurity diffusion in oxidizing ambients

The linear diffusion equation may be transformed to a moving reference frame which corresponds to a linear-parabolic or experimental oxide growth law. The resulting partial differential equation is separable and may be Laplace transformed. If the semiconductor is initially uniformly doped and semi-infinite, solutions in the Laplace transform domain are expressible as parabolic cylinder functions. Integration constants for constant interface concentration or deposition diffusions as well as leaching boundary conditions may be determined.A space-time solution for the deposition problem is derived. Leaching from a uniformly doped substrate is treated in some detail. Residue techniques are used to develop analytic expressions for the dominant solution term, which is compared to published results. The complete solution may be obtained by using approximate analytic inversion, which requires numerical computations. Results are compared with data from existing theories, which are special cases of the present model.     

Accurate and efficient numerical integration of weakly singular integrals in Galerkin EFIE solutions

A Galerkin descretization of the electric field integral equation for perfectly conducting surfaces using Rao-Wilton-Glisson (1982) basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions. These singularities have been traditionally handled by utilizing a "singularity extraction" procedure to produce a regular integral and an analytic function to replace the original singular integral. A new approach is presented here in which the four-dimensional (4-D) weakly singular integrals unique to the Galerkin Rao-Wilton-Glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands. The transformations allow some of the integrations to be performed analytically, in some cases reducing the original 4-D integral into a 1-D numerical integration. The accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle.     

Forming electrodes for bipolar beams shaped as strips and solid or hollow cylinders

The configuration of forming electrodes for strip and cylindrical bipolar beams is calculated. The method applied for strip beams is based on the exact parametric equations of equipotential surfaces. An analytic extension of the equation for a planar diode and a solution to Laplace’s equation are used in the case of cylindrical beams. The solution to Laplace’s equation is represented in an integral form. The results obtained are compared to approximate solutions to the corresponding problems. The decompositions describing the explicit equations of the zero equipotential surfaces in axially symmetric and plane systems are analyzed. The behavior of these decompositions makes it possible to extend the results to 3D problems for beams having more complicated shapes.     

A Method for the Calculation of the Radiation-Pattern and Mode-Conversion Properties of a Solid-State Heterojunction Laser

A solution of the laser fields, both inside and outside the laser, is given in terms of the mode-conversion coefficients and an integral equation for the radiation pattern. It is shown how very accurate analytic solutions can be obtained by what, at first sight, appear to be extremely crude approximations. The reason is that mode conversion is taken implicitly into account by using a multiplier, whose exact form does not appear to be very critical, as a weighting function to average two different formulas for the function representing the radiation; and with the correct form for it, all the mode-conversion and reflection coefficients can be legitimately ignored. A plane-wave formula for this multiplier is a good first approximation, and a number of existing expressions occurring in the literature are obtained in this way. It is also shown rigorously that the results of an earlier obliquity-factor analysis apply. Further refinements are introduced to allow for higher order discrete modes, and good approximate analytic forms for the mode-reflection and conversion coefficients are obtained. A check with a rather extreme example shows excellent agreement with Ikegami's numerical computation for the dominant-mode reflection at the laser-air interface. The methods of this paper are applicable to general laser structures of cylindrical geometry with either continuous or discontinuous variations in refractive index. Very accurate numerical solutions should be obtainable after only one iteration of the integral equation, starting with the reflection-modified form of Hockham's formula as initiating function.     

分析介质光波导传播特性的Cole—Hopf变换法

采用Cole-Hopf变换法，将平板光波导导模所满足的二阶常微分方程（Helmholtz方程）变换成一阶常微分方程（Riccati方程），用较简单且有效的方法分析导模的特性。给出了多层阶跃型及渐变型平板波导导模的精确解析解和数值解法及实例；给出了非线性平板波导传播特性的数值计算法及实例。