HIGHER ORDER NORMAL FORM AND PERIOD AVERAGING

Calculation of the higher order averaging equations of a non-linear oscillator is very tedious using the classical averaging method. This is also true for higher order normal forms. This paper presents an alternative method, which is a combination of the method of normal form and the classical averaging method. A simple and efficient program is given to calculate the higher order averaging equations by using the symbolic computer algebra system Mathematica. Furthermore, the program can be used to calculate the higher order coefficients of normal form. Four examples are given and compare well with the existing results.     

高阶Broer-Kaup(BK)方程组的新精确解

利用扩展齐次平衡法,我们得到了1+1维和2+1维高阶BK方程组新的孤子解和无穷多有理函数解,尤其是求出了初始值问题解的封闭形式.     

SOME NEW AND EXACT EXPLICIT SOLUTIONS OF THE HIGHER ORDER BROER-KAUP EQUATIONS

A simple solitary wave solution and infinitely many rational function solutions, especially the closed form of the solution for the initial value problem of the higher order Broer-Kaup (BK) systems in (1+1) and (2+1) dimensions, are obtained by using the extended homogeneous balance method.     

STATISTICAL ENERGY ANALYSIS OF COUPLED PLATE SYSTEMS WITH LOW MODAL DENSITY AND LOW MODAL OVERLAP

Finite element methods, experimental statistical energy analysis (ESEA) and Monte Carlo methods have been used to determine coupling loss factors for use in statistical energy analysis (SEA). The aim was to use the concept of an ESEA ensemble to facilitate the use of SEA with plate subsystems that have low modal density and low modal overlap. An advantage of the ESEA ensemble approach was that when the matrix inversion failed for a single deterministic analysis, the majority of ensemble members did not encounter problems. Failure of the matrix inversion for a single deterministic analysis may incorrectly lead to the conclusion that SEA is not appropriate. However, when the majority of the ESEA ensemble members have positive coupling loss factors, this provides sufficient motivation to attempt an SEA model. The ensembles were created using the normal distribution to introduce variation into the plate dimensions. For plate systems with low modal density and low modal overlap, it was found that the resulting probability distribution function for the linear coupling loss factor could be considered as lognormal. This allowed statistical confidence limits to be determined for the coupling loss factor. The SEA permutation method was then used to calculate the expected range of the response using these confidence limits in the SEA matrix solution. For plate systems with low modal density and low modal overlap, relatively small variation/uncertainty in the physical properties caused large differences in the coupling parameters. For this reason, a single deterministic analysis is of minimal use. Therefore, the ability to determine both the ensemble average and the expected range with SEA is crucial in allowing a robust assessment of vibration transmission between plate systems with low modal density and low modal overlap.     

一种高阶重力场方程及其静态球对称解

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广义五阶KdV方程的孤波解与孤子解

利用求解非线性代数方程组的吴文俊特征列方法,借助计算机代数系统获得了一类较广泛的五阶非线性演化方程的孤波解和孤子解,修正和完善了已知的结论 关键词： 五阶KdV方程 孤波 孤子解     

KdV方程与高阶KdV方程行波解之间的形变理论

从具有较多参数的复杂非线性方程的解出发,取某些参数的极限,这些解就退化到具有较少参数的简单方程的解,本文以KdV方程的行波解为例说明对于某些特解,上述极限过程的逆过程,即将简单方程的解形变到复杂方程的解是可能的,但一般来说并不一定具有唯一性。 关键词：     

磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合

本文采用Hasegawa-Wakatani方程组研究磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合。求得非线性方程组的偶极涡旋解。这些解属于本性电磁涡旋,对应的扰动磁场和纵向电流在涡旋边界上是连续的。 关键词：     

一维周期耗散媒质中的电磁波模及其数值分析

文中推导了一维周期耗散媒质中电磁波模式特征值方程,证明其解分类为一系列的"导带"和"禁带";用实数Re(K_z²)代替复特征值K_z标识模式,可清晰地显示出带结构,便于模式的分类和比较。文中用数值方法给出了几组参数下横电波、横磁波模最低两个带的图示,并与周期势场中的电子能带作了对比。     

自由电子激光中电子与辐射波相互作用有效时间的分析

利用已获得的大信号自由电子激光增益公式,导出了激光平均增长率表达式,分析了自由电子激光中电子与辐射波相互作用的有效时间,讨论了其主要物理参量对相互作用有效时间的影响 关键词：     

硅酸铋晶体内电光、磁光相互作用的耦合波分析及其传感应用

通过建立并求解硅酸铋(BSO)晶体内电光、磁光相互作用的耦合波方程,得到了BSO晶体的偏振传递函数,由此分析了BSO晶体内偏振光的周期性变化规律,并给出直接描述外加电场、磁场对偏振光作用的琼斯矩阵和米勒矩阵.最后设计了一种基于BSO晶体的电压、电流同时传感系统.     

四维Minkowski空间中具有立方非线性复标量场方程的平面与球面波解

本文在四维Minkowski空间中对具有立方非线性复标量场方程进行了研究,并给出了场方程的两种精确解,这两种解相当于场的平面与球面波解。 关键词：     

ON THE ROLES OF COMPLEMENTARY AND ADMISSIBLE BOUNDARY CONSTRAINTS IN FOURIER SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS OF COMPLETELY COUPLED r TH ORDER PDES

A heretofore unavailable double Fourier series based approach, for obtaining non-separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions, has been presented. The method has been successfully implemented to solve a class of hitherto unsolved boundary-value problems, pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform, with arbitrarily prescribed (both symmetric and asymmetric with respect to the panel centerlines) admissible boundary conditions and subjected to general transverse loading.Existing solutions such as those due to Navier or Levy are based on the well-known method of separation of variables. Such solutions represent particular solutions whenever the method of separation of variables work, and when these particular solution functions fortuitously satisfy the boundary conditions. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form sets of measure zero.Various cases of lamination, geometry and dynamic response (forced and free vibrations) of a class of thin anisotropic laminated shells (curved panels) have been shown to follow from the above. Six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions. Navier-type solutions whenever available form special cases of the present general solution.     

平面电磁波在任意方向运动的介质-介质界面上的反射和透射

研究平面电磁波从一种介质入射到另一种以任意方向运动的介质时,在介质界面上发生的反射和透射现象,从Maxwell方程组、运动界面的边值关系和运动介质的本构关系出发,得到了反射波和透射波电磁场矢量与入射波电磁场矢量的关系的表达式、反射和透射系数,讨论了反射波、透射波与入射波之间的能量关系,电磁波对运动介质作用力的性质,并得出一些新的结论． 关键词：