用三角级数和Maple软件求Burgers方程的精确解

用三角级数试探求解Burgers方程,得到关于待定系数的非线性代数方程组,利用Maple软件求解此非线性代数方程组,进而求得Burgers方程的精确解.     

Exact solutions of （3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.     

Superposition solitons in two-component Bose-Einstein condensates

We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose-Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.     

A Kind of Exact Inflationary Solution in the Chaotic Inflation Model to Non-minimally Coupled Scalar Field

We present a kind of exact inflationary solution in the chaotic inflation scenario to non-minimal coupled scalar field, taking the Hubble parameter directly as a function of the scalar field φ, H（φ） = αφ^n. Using the analysis of the WMAP3 data, we give the range of power index n.     

Singular Wave Solutions of Two Integrable Generalized KdV Equations

We present some singular wave solutions such as multi-peaked periodic waves, multi-peaked kink waves, multi-peaked peakons as well as kink-compactons, associated with singular curves of generalized KdV equation and modified KdV equation. When a trajectory intersects with the singular curve, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed.     

基于模糊博弈视角的企业联盟“双循环”合作对策研究

企业合作在“双循环”新发展格局下呈现出更多的模糊特征,能否形成稳定的模糊合作格局及持续合作的收益再分配策略成为合作联盟的关注点。将广义模糊超量博弈和模糊凸博弈及其广义解集应用到“双循环”新发展格局下企业联盟合作与收益再分配中,提出最大广义模糊超量博弈模型及其广义模糊谈判集,并基于最大广义模糊超量博弈均衡性的视角,对模糊凸博弈下广义模糊谈判集与核心的等价性质进行论证。研究结果不仅满足了“双循环”新发展格局下合作企业以部分资源参与合作的意愿,及企业联盟模糊凸合作博弈下再分配方案等价性证明需求,而且实现了保留部分收益用于联盟再发展的策略。     

一个非线性方程的显示行波解

利用双曲函数法和吴元代数消元法,获得了Ｒ－Ｌ－Ｗ方程的多组行波解,其中包括新的行波解、有理函数形式的行波解。     

爱因斯坦方程的一组严格的双孤立波解

由一个对角型的度规出发,给出了一组严格的引力双孤立波解。这组解是处处正则和稳定的,它们描写两个分别沿正z方向和负z方向的光速传播的孤立波,而且在彼此碰撞后不会改变自己形状并继续传播,文章最后还讨论了这组解相应的时空奇异性和能量正定性问题。 关键词：     

Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

基于解析法的超导发电机磁场分析与结构优化

混合型高温超导发电机采用高温超导带材作励磁材料,结构上与传统电机有较大的不同,设计方法也不尽相同.本文基于傅里叶变换将超导发电机的励磁集中绕组等效为沿转子圆周正弦分布的激励源,建立了超导发电机磁场分析模型.对电机气隙磁场分布进行了求解,并分析了不同绕组张角时气隙磁密波形中的谐波含量.通过参数化分析,研究了不同环境屏、转子的尺寸对电机功率密度的影响.采用有限元法对磁场求解结果进行了验证,结果一致性较好.研究结果表明,励磁绕组张角会对电机气隙磁密波形产生影响,合理设置超导发电机环境屏及转子结构,可以提高超导发动机的功率密度.