两个非线性方程的势对称及其不变解

通过计算NTT方程和Burgers方程的势对称扩大了其古典对称,并获得了 Burgers 方程的一系列新的精确解. 首先,基于微分特征列集算法确定了NTT方程和Burgers方程的古典对称和势对称,并确定了 Burgers 方程的两个势对称对应的单参数Lie变换群. 其次,利用推广的简单方程方法构造了 Burgers方程的不变解,这些解分别以含任意两个参数的双曲函数、三角函数和有理函数表示. 最后,将势对称对应的Lie变换群(14)作用于Burgers方程的不变解上获得了新的精确解,重要的是这些解都不能由方程的古典对称得到.     

基于雷达方程修正的目标探测距离评估方法

针对现有的雷达方程在评估对海雷达最大探测距离上与实际不符的问题,提出了在一般方程的基础上,利用实测数据来修正方程的方法。分析了一般雷达方程应用的局限性,根据试验中海杂波对目标探测的影响,简化一般方程为信杂比方程。利用X波段对海探测雷达的试验数据,对信杂比方程进行修正,克服了方程在实际应用的不足,使方程能够满足该类型雷达对目标的最大探测距离的计算。计算结果表明,修正后方程计算的结果与雷达显示的结果基本相同。     

Efficient numerical techniques for solving Pocklington's equation and their relationships to other methods

It is shown that testing Pocklington's equation with piecewise sinusoidal functions yields an integro-difference equation whose numerical solution is identical to that of the point-matched Hallen's equation when a common set of basis functions is used with each. For any choice of basis functions, the integro-difference equation has the simple kernel, the fast convergence, the simplicity of point-matching, and the adequate treatment of rapidly varying incident fields, but none of the additional unknowns normally associated with Hallen's equation. Furthermore, for the special choice of piecewise sinusoids as the basis functions, the method reduces to Richmond's piecewise sinusoidal reaction matching technique, or Galerkin's method. It is also shown that testing with piecewise linear (triangle) functions yields an integro-difference equation whose solution converges asymptotically at the same rate as that of Hallen's equation. The resulting equation is essentially that obtained by approximating the second derivative in Pocklington's equation by its finite difference equivalent. The authors suggest a simple and highly efficient method for solving Pocklington's equation. This approach is contrasted to the point-matched solution of Pocklington's equation and the reasons for the poor convergence of the latter are examined.     

Experimental Demonstration of the Corbella Equation for Aperture Synthesis Microwave Radiometry

The fundamental equation of aperture synthesis microwave radiometry has been recently revised into a new so-called Corbella equation to include antenna coupling effects and the interferometry formulation into a single equation. This equation has been experimentally demonstrated for the first time with a full prototype of the Microwave Imaging Radiometer with Aperture Synthesis. Several tests have been carried out to demonstrate the new visibility equation with different targets. The test results show better agreement with simulations based on the Corbella equation than the old fundamental equation. An initial analysis of the influence of the antenna pattern characterization errors shows the importance of these errors in the final results according to the new formulation     

Numerical analysis of surface wave on microstrip antenna with lossysubstrate

The key to analysing a guided surface wave is to solve its eigenvalue equation. When the medium is dissipative, the eigenvalue equation is a complex transcendental equation. The Kuhn algorithm is applied to work out the eigenvalue equation     

均匀随机媒质中传播的波——有不同波数的m-n阶矩方程的解

在研究随机媒质中传播的波的一些有关问题时,常常需要求解波的矩方程。具有不同波数的m-n阶矩方程是一个抛物近似的偏微分波动方程。本文应用格林函数方法将偏微分方程变为积分方程,并用迭代法求得了该积分方程的解。同时,又应用接连散射的方法求解了具有不同波数的m-n阶矩方程,两种方法所得的结果完全相同。文中对解的物理含义作了说明,并讨论了用于波传播研究中的一些问题。     

Caudrey–Dodd–Gibbon–Kotera–Sawada方程的对称、精确解和守恒律

应用改进的CK直接方法,得到了（2+1）维Caudrey–Dodd–Gibbon–Kotera–Sawada（CDGKS）方程的对称群定理。利用对称群理论和方程的旧解得到了该方程新的精确解,扩大了解的范围。最后根据对称和共轭方程求出了（2+1）维CDGKS方程的无穷多守恒律。     

随机非线性系统自由状态方程的任意阶近似解

针对非线性系统的随机性的特点,提出了随机非线性系统自由状态方程的任意阶近似解法.该解法从自由状态空间中的广义朗之万梯度方程出发,利用常数变易法导出了与广义朗之万方程等价的广义的第二类非线性、随机性Valterra积分方程,采用逐次逼近法求得了方程的任意阶近似解.最后,讨论了非线性、随机性对系统状态空间转移的影响.随机非线性系统自由状态方程的任意阶近似解法为随机非线性系统的定量分析提供了一种有效方法.     

放电泵浦XeCl激光的理论模型

本文对传输线作电源的自持放电XeCl激光进行动力学分析,给出电子能量分布玻尔兹曼方程、能量平衡方程、电子线路方程及激光振荡方程的数值解,并与实验结果作了比较。     

广义网孔方程建立算法研究

为了探究广义网孔方程建立规范和方法,对含有公共电流源支路电路的网孔方程进行详细的理论分析,探寻了广义网孔方程的构成规律,得到了广义网孔方程的建立算法,该算法具有普适性。在应用网孔分析法分析含有公共电流源支路的电路问题时,在不引入辅助解变量的情况下,利用该算法可快捷地建立起广义网孔方程,提高了分析和求解效率。由实例证明,广义网孔方程建立算法是正确的、有效的,是对网孔分析法的一种推广和完善。     

Tunable laser optics: Applications to optics and quantum optics

Optics originally developed for tunable organic dye lasers have found applications in other areas of optics, laser optics, and quantum optics. Here, the salient aspects of the physics related to the cavity linewidth equation and the effects of intracavity beam expansion and intracavity dispersion on this equation are reviewed. Additionally, the generalized multiple-prism dispersion equation is applied to direct-vision prisms, also known as Amici prisms, to calculate dispersion configurations of practical interest. Then, the higher derivatives of the multiple-prism dispersion equation applicable to laser pulse compression are considered. From this perspective, a new compact and generalized equation for higher-order phase derivatives is introduced for the first time. Furthermore, it is shown how the N-slit interferometric equation, derived from quantum principles using Dirac's notation, gives rise to generalized versions of the diffraction grating equation and the law of refraction. The nexus between the N-slit interferometric equation and the cavity linewidth equation is also illustrated. Finally, various optical and quantum optical applications that have benefited from these developments are highlighted.     

薛定谔方程中包络孤子运动及相互作用的辛算法模拟

给出并证明了薛定谔方程中高斯包络孤子的表达式.针对该高斯包络孤子进一步提出了薛定谔方程中存在高斯包络孤子相互作用的情况;针对薛定谔方程提出其辛算法.通过分离波函数实部和虚部把薛定谔方程变换成标准的哈密顿正则方程组,对正则方程进行欧拉中心差分离散实现辛算法.给出了辛算法的守恒量,并证明了其稳定性.对薛定谔方程中的高斯包络孤子运动及多孤子相互作用过程进行了数值仿真,实验结果证明了所提观点的正确性及辛算法的有效性.     

Generalizations of the Klaassen-Prins equation for calculating the noise of semiconductor devices

The Klaassen-Prins equation is the standard equation for calculating the drain thermal noise of long-channel MOSFETs. We show that the Klaassen-Prins equation is not always valid, even for MOSFETs. We present generalizations to the Klaassen-Prins equation that include velocity saturation effects of short-channel MOSFETs and that comprise also induced gate noise.     

均匀随机媒质中传播的波有不同波数的m-n阶矩方程的解

在研究随机媒质中传播的波的一些有关问题时,常常需要求解波的矩方程。具有不同波数的m-n阶矩方程是一个抛物近似的偏微分波动方程。本文应用格林函数方法将偏微分方程变为积分方程,并用迭代法求得了该积分方程的解。同时,又应用接连散射的方法求解了具有不同波数的m-n阶矩方程,两种方法所得的结果完全相同。文中对解的物理含义作了说明,并讨论了用于波传播研究中的一些问题。     

带强迫项的KdV方程的非线性自伴随性和守恒律

应用非线性自伴随性的概念和伊布拉基莫夫的一般守恒律定理，研究了带强迫的KdV方程的非线性自伴随性和守恒律。首先讨论了自伴随性，结果表明这个方程具有非线性自伴随性，同时得到了这个方程的形式拉格朗日量。在对这个方程进行李对称分析之后，根据李对称的不同得到了这个方程的一些非平凡守恒律。     

Transient excitation of a straight thin-wire segment: a new look atan old problem

The transient excitation of a straight thin-wire segment is analyzed with the aid of a one-dimensional integral equation for the current along the wire. An almost exact derivation of that equation, in which only the radial current on the end faces is approximated, is given. The integral equation obtained turns out to be identical to the reduced version of Pocklington's equation. On the basis of this derivation, existing and new numerical solution techniques are critically reviewed. Pocklington's equation and Hallen's equivalent form are solved directly by marching on in time as well as indirectly via a transformation to the frequency domain. For Pocklington's equation, a conventional moment-method discretization leads to a Toeplitz matrix that is inverted with Levinson's algorithm. For Hallen's equation, the Toeplitz structure is disturbed, and the frequency-domain constituents are determined with the aid of the conjugate-gradient-FFT method. Illustrative numerical results are presented and discussed     

Integral-equation approach to the abrupt-depletion approximation in semiconductor components

By using the abrupt-depletion approximation, one obtains a linear equation for the minority-carrier concentration in a semiconductor. This equation describes the diffusion and the recombination statistics of the carriers under steady-state conditions. In a 2-dimensional geometry, this equation can be replaced by an equivalent integral equation, so that the given problem can be easily solved numerically.     

Transformation of `bandpass? linear time-variant system into equivalent `lowpass? system

It is shown that a type of `bandpass? linear time-variant differential equation has an equivalent `lowpass? linear time-variant differential equation. The solution of the equivalent equation by computational techniques may proceed at a much higher rate than solution of the original equation, and offers simple computation of the amplitude and phase of the system narrowband response.     

Modified scheme for simulation of a delayor for polynomial inputs

The steady-state response of any differential equation is a polynomial of the same degree as the input if the coefficients of the differential equation are so chosen that all the roots of the characteristic equation have nonzero negative real parts. If the order of the differential equation is the same as the degree of the input function, then under the steady-state condition the input and its derivatives can he obtained from the output and its derivatives which are readily available from the analog setup simulating the differential equation. From this a delayed or an advanced function can he generated by using Maclaurin's series expansion. The transient period of the scheme can be adjusted by a proper choice of the coefficients of the differential equation.     

The electron beam in a cathode-ray tube

The beam in a cathode-ray tube is described by a "paraxial" Liouville equation. This equation takes into account the thermal spread of the electrons as well as the influence of the space charge of the beam. The solution of this equation is given. An ordinary differential equation is derived for the beam radius. The equation has been solved in the field-free region outside the gun. The result is presented in graphs which can be applied to the determination of the spot size on the screen of a cathode-ray tube.