(2+1)维一般Calogero-Bogoyavlenskii-Schiff系统的无穷序列类孤子新解

为了构造(2+1)维一般Calogero-Bogoyavlenskii-Schiff系统的无穷序列类孤子新解,首先引入了可转化为Riccati方程的新的辅助方程及其新解,其次给出了Riccati方程的新解、Bäcklund变换和解的非线性叠加公式。在此基础上,借助符号计算系统Mathematica, 构造了(2+1)维一般Calogero-Bogoyavlenskii-Schiff系统的无穷序列类孤子新解。这些解由指数函数,三角函数和有理函数复合组成。     

sine-Gordon型方程的Jacobi椭圆函数精确解

给出一种三角函数型辅助方程及其解,并借助符号计算系统Mathematica,把该方程直接应用到sine-Gordon方程、双sine-Gordon方程和MKdV-sine-Gordon方程,得到了Jacobi椭圆函数精确解以及退化后的孤波解和三角函数波解.     

构造非线性演化方程精确解的一个新方法

基于辅助方程提出一种求解非线性演化方程的一个新方法,该方法简单易行且具有一定的普适性,根据不同的参数可给出各种形式的精确解,从而有助于探索非线性方程的新解及其性质。并以mkdv方程为例,得到了其多组精确解,包括Jacobi椭圆函数解及Weierstrass椭圆函数解等,除涵盖了以往结果,还给出一些新解。     

广义变系数五阶KdV和BBM方程的孤立子解

利用假设孤立波方法,研究了广义变系数五阶KdV方程和BBM方程,得到了广义变系数五阶KdV方程和BBM方程的孤立子解。对于得到的孤立子解,为了保证解的存在性,给出了孤立子解存在的条件。     

(2+1)维Boiti-Leon-Manna-Pempinelli方程的对称、精确解及守恒律

利用李群分析方法,得到了(2 1)维Boiti-Leon-Manna-Pempinelli(BLMP)方程的对称、相似约化和新的精确解,包括有理函数解、双曲函数解、雅克比椭圆函数解和三角周期解.同时找到了此方程的无穷多守恒律.     

（3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解

利用直接对称方法得到了广义KdV-Zakharov-Kuznetsev方程（简写为mKdV-ZK）的对称约化、精确解，其中包括椭圆函数解，幂级数解，艾米儿函数解等. 利用得到的对称，求出了该方程的守恒律.     

推广的简单方程方法对 Whitham-Broer-Kaup-Like 方程组的应用

应用推广的简单方程方法成功构造了Whitham-Broer-Kaup-Like方程组的新的精确行波解. 这些行波解分别以含有双参数的双曲函数, 三角函数和有理函数表示. 当双曲函数表示的行波解中参数取特殊值时可得孤波解. 得到的结果说明了推广的简单方程方法函数方法是直接、可靠和行之有效的方法, 并且该方法也可用于求解数学物理中的其它非线性发展方程的更多精确行波解.     

Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope

Employing a variable coordinate system associated with the local features of two-dimensionally rough surfaces with arbitrary slope, full-wave solutions are derived for the depolarization of the scattered radiation fields. An outline of the analytical procedures used in the derivations of the solutions are presented. Furthermore, the engineer who is not familiar with them can also use the final result which is expressed as a definite integral whose integrand is given explicitly and in closed form. These full-wave solutions are compared with the quasi-optics solution and the iterative or perturbational solutions for slightly rough surfaces, and they are shown to bridge the wide gap that exists between them. The full-wave solutions are consistent with energy conservation, duality, and reciprocity relationships in electromagnetic theory. These solutions account for upward and downward scattering of the incident waves with respect to the horizontal reference plane, thus shadowing and multiple scattering are considered. Applications to two-dimensionally periodic structures and random rough surfaces are also presented. The fullwave solutions are examined for Brewster, grazing, and specular angles and backscatter. Special consideration is also given to good conducting boundaries.     

(2+1)维色散长波方程组新的无穷序列精确解

为了获得非线性发展方程的无穷序列新精确解, 给出Riccati方程的一些新解和B\"{a}cklund变换以及解的非线性叠加公式, 并Riccati方程与函数变换相结合,借助符号计算系统Mathematica,构造了 (2+1)维维色散长波方程组新的无穷序列精确解. 这些解包括无穷序列类孤子解、无穷序列复合型解等. 这种方法构造非线性发展方程无穷序列精确解领域具有普遍意义.     

Full wave analysis for rough surface diffuse, incoherent radarcross sections with height-slope correlations included

The bistatic scattering cross sections are derived for rough one-dimensional perfectly conducting surfaces using the full wave approach. The surfaces are characterized by four-dimensional Gaussian joint probability density functions for heights and slopes. Thus, correlations between the rough surface heights and slopes are accounted for in the analysis. Convergence of the formal series solution is considered. Self-shadowing effects are included. The full-wave solutions are compared with the small perturbation solutions, which are polarization dependent, and the specular point (physical optics) solutions, which are independent of polarization. Both the physical optics and the small perturbation solutions can be obtained from the full-wave solution     

Surface integral representations for electromagnetic scattering from dielectric cylinders

The surface integral representations are derived for electromagnetic wave scattering from dielectric bodies. Several kinds of integral equations are given for dielectric cylinders immersed in an obliquely incident wave. The interior resonant solutions, the cause of erroneous solutions, accompanied with the equations presented here and the removal of these solutions are briefly discussed.     

应用改进的G’/G~2展开法求Zakharov方程的精确解

应用改进的G’/G~2展开法构造出Zakharov方程的18组精确解,这些解主要包括双曲函数通解、三角函数通解和有理函数通解三种形式.当对双曲函数通解中的参数取特殊值时,可以得到孤立波解.对三角函数通解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,应用改进的G’/G~2展开法能够得到Zakharov方程一些新的精确解,扩大了解的范围,这种方法对于研究非线性光学和量子光学具有非常广泛的应用意义。     

一种计算无损传输线上电压、电流解析解的方法

直接求解无损传输线方程所得的通解包含了正向行波和反向行波两部分。本文在此基础上根据行波在传输线上多次反射的现象。推导出了在阶跃激励下无损传输线上任意一点的解析解,并对线上电压、电流的稳态值作了讨论。同时,该方法更加清晰地描述了线上电压和电流行波的暂态过程,更能体现出通解的物理含义。     

应用改进的G/G展开法求ZS方程的精确解

应用改进的G/G展开法构造出Zhiber-Shabat(ZS)方程的20组精确解,这些解的类型主要包含双曲函数通解、三角函数通解和有理函数通解三种形式。对解的性质进行了相应分析,当对双曲函数通解中的参数取特殊值时,可以得到孤立波解。当对三角函数通解中的参数取特殊值时,可以得到对应的周期波函解。实践证明,应用改进的G/G'展开法能够得到方程一些新的精确解,扩大了解的范围。     

(2+1)维Broer-Kaup-Kupershmidt方程的精确解

文章得到了一个辅助微分方程的一些新解,利用该辅助方程直接求解了(2 1)维Broer-Kaup-Kupershmidt方程,结果获得了该方程的一些新的孤立波解和周期解.     

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.     

Resonant solutions involved in the integral equation approach to scattering from conducting and dielectric cylinders

Resonant solutions involved in the integral equation formulation for analyzing the scattering problems and the elimination of these erroneous solutions are investigated. The parameter ranges where the resonant solutions are mixed into the correct ones and the degree of errors caused by the resonant solutions are checked on through numerical computation of matrix condition numbers and scattering cross sections for dielectric cylinders of square cross section with side width/wavelength ratio being less than about 1.27. As a method of removing the resonant solutions, the method taking some lower order equations of the so-called "extended boundary condition (EBC) method" into consideration is proposed.     

Toward a CPFLOW-based algorithm to compute all the type-1 load-flow solutions in electric power systems

This paper presents a potential algorithm based on continuation power flow (CPFLOW) to compute all the Type-1 load-flow solutions. Type-1 solutions are of a single positive real-part eigenvalue associated with Jacobian of load-flow equations and are used in conjunction with techniques such as energy methods and the voltage instability proximity index (VIPI) for assessing system voltage stability. The benefits of the proposed algorithm are the following. The algorithm has the potential to find all the Type-1 load-flow solutions by tracing a small number of homotopy curves. Traditional methods, which can locate some of the Type-1 solutions, suffer from the uncertainty that there might be another Type-1 solution that might be more suitable for voltage stability assessment. This uncertainty is eliminated if all the Type-1 solutions are located. The proposed algorithm has been tested for two example systems, and encouraging results have been obtained.     

变系数(3+1)维Zakharov-Kuznetsov方程的Jacobi椭圆函数精确解

给出了第一种椭圆方程的一些新解和解的非线性叠加公式,然后与一种函数变换相结合, 借助符号计算系统Mathematica,构造了变系数(3+1)维Zakharov-Kuznetsov方程的类Jacobi椭圆函数精确解以及无穷多个类孤子解和三角函数解。     

Ray-Transformation Conditions and Shaped-Reflector Solutions for Three-Reflector Optics Without Cross Polarization

Reflector synthesis in geometric optics is extended to three-reflector systems producing field transformations that are spherical-to-planar in wavefront, of a prescribed form in power pattern and zero in cross polarization. Necessary and sufficient conditions for the existence of solutions are derived in terms of the input-to-output ray transformation and the surface of either the input or output reflector. A subset of the conditions, for a class of non-unique solutions, is interpreted geometrically in terms of the principal directions of the ray transformation and the lines of field polarization and wavefront curvature. These conditions are then used to derive integral solutions for offset-fed reflectors with any prescribed rotationally-symmetric power-pattern transformation. The reflector solutions are shown to exist for a continuous range of offset parameters, take the form of congruences of ellipses and include a special case where the main reflector is paraboloidal. Low-aberration solutions satisfying Abbe's sine condition are obtained in terms of standard functions. Illumination-enhancing solutions illustrate a possible application to compact-range illuminators for antenna measurements.