氘氚燃烧等离子体的热不稳定性计算

由于氘氚反应率与离子温度有很强的依赖关系，氘氚燃烧等离子体是热不稳定的。讨论了描述稳态氘氚燃烧等离子体功率平衡方程的非线性特征。利用打靶方法，可以求得态温度分布和关于温度微扰方程的本征值。可是，由上述方法得出的平衡解会与随时间变化方程在ｔ→∞时的解不一致，这是一类未解决非线性数学问题的一个典型例子。     

Coupled Nonlinear Schrodinger Equation： Symmetries and Exact Solutions

The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.     

Solitary Wave and Wave Front as Viewed From Curvature

The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometrically, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s), which varies with arc length s. For solitary wave when s → ±∞, then its curvature c(s) approaches zero, and when s=0, the curvature c(s) reaches its maximum. For wave front, when s → ±∞, then its curvature c(s) approaches zero, and when s=0, the curvature c(s) is still zero, but c'(s) ≠ 0. That is, s=0 is a turning point. When c(s) is given, the variance at some point (x,y) in stream line with arc length s satisfies a 2-order linear variable-coefficient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front.     

A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation

A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein－Gordon equation.     

Calculation of geometrical birefringence from two-dimensional refractive-index profile in single-mode fibres

We present two numerical approaches to calculate the geometrical birefringence from two-dimenslonal refractive-index profile in single-mode fibres. One is the improved perturbation model theory, the other is based on the general solution of noncircular uniform optical waveguide in an arbitrary coordinate system. Using these methods, we can obtain not only the magnitude of geometrical birefringence, but also the orientation of birefrlngent axes. We report the calculation results of geometrical birefringence in a real single-mode fibre.     

非线性Schroedinger方程的包络形式解

扩展了最近提出的F展开方法以构造非线性演化方程更多的精确解，即将F展开法中的一阶非线性常微分方程和单变量的有限幂级数代之以类似的一阶常微分方程组和两个变量的有限幂级数，这两个变量是一阶常微分方程组的解分量．作为例子，用扩展的F展开法解非线性Schroedinger方程，得到了很丰富的包络形式的精确解，特别是以两个不同的Jacobi椭圆函数表示的解．显然，扩展的F展开方法也可以解其他类型的非线性演化方程．     

基于椭圆型方程的扭叶片造型方法的研究

本文以偏微分方程造型为基础,提出了一种基于椭圆型方程的扭叶片三维型面直接设计方法,详细推导了叶型曲面函数,给出了型面方程的求解及其前后缘修正。该方法具有设计叶型曲面自然光顺,设计参数少且各参数具有明显的几何意义,叶型曲面调整方便,利于采用非数值优化算法对其进行气动优化等优点。文中给出了设计实例,并通过数值实验分析了所设计叶片型面的流动特性。分析结果表明设计叶片具有良好的气动性能,同时也证明了本文提出的基于椭圆型方程的扭叶片三维型面设计方法的可靠性和实用性。     

Extra Dimensions and Vacuum Dark Energy Models

The role of vacuum energy or cosmological constant in cosmology is discussed in a kind of nontrivial higherdimensional model. Under the framework of Einstein‘s gravity, we obtain the corresponding equations of motion and find that the cosmological constant and vacuum energy in the full regime does not drive its acceleration, but decelerates the expansion of the universe. The dimension of space is required to be n = 3 if we regard vacuum energy or cosmological constant as the candidate to drive the accelerated expansion of the universe.     

一类分数阶混沌金融系统的复杂性演化研究

物理学理论与方法在经济与金融领域中的成功应用催生了一个新的科学分支——经济物理学(econophysics).分数阶微积分系统的复杂动力学现象受到了越来越多学者的关注.本文定性地分析一类分数阶混沌金融系统的均衡解的稳定性及Hopf分岔发生的条件,并运用亚当斯-巴什福斯-莫尔顿预估-校正的有限差分法,通过分岔图、相图和时间序列图对该系统的复杂性演化行为进行仿真研究. 关键词： 经济物理学 分数阶微分方程 金融模型 混沌