Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic: equation is taken as a transformation and is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.     

高剪切率的Couette流下液氩流体热导率的分子动力学模拟

基于平衡分子动力学(EMD)模拟方法,对Lees-Edwards周期性边界条件作一修正并成功地应用其形成具有高恒定剪切率的Couette流动,最后通过Green-Kubo公式计算得到了剪切流下液氩流体的热导率。计算结果,表明在剪切流下液氩流体的热导率仍然表现为各向同性,同时还发现流动方向的热导率不随流动剪切率的增加而发生变化,并且该值跟静态下液氩的热导率(λ=0.132 Wm~(-1)K~(-1))基本一致。     

周期轨迹与不可积体系的量子化：Henon-Heiles体系的一个研究例子

研究了两个振子耦合的Henon-Heiles体系的周期轨迹与量子化问题.结果表明，周期轨迹的 作用量积分与体系的能量有着简单的线性关系.可以利用那些是整数值的周期轨迹的作用量 积分对不可积体系进行半经典量子化.由周期轨迹的物理内涵出发，揭示混沌体系的残余周 期轨迹具有与量子化有关的性质.这对于认识和理解经典力学与量子体系的联系关系及其物 理内涵有着深刻而重要的意义. 关键词： 周期轨迹 半经典量子化 混沌     

Absolute Continuity in Periodic Thin Tubes and Strongly Coupled Leaky Wires

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficiently strongly attractive interaction supported by a periodic curve in R^d = 2, 3.     

立方非线性Schr?dinger方程的Weierstrass椭圆函数周期解

利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性 Schr(o)dinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组).     

准相位匹配PPKTP晶体连续倍频13 mW绿光输出

采用高压脉冲电场极化,通过电光效应实时监控、倍频通光二维监控等手段的应用,制备出周期为9μm、长为8 mm、宽为3 mm、厚为1 mm的周期极化KTiOPO4晶体(PPKTP);倍频通光实验中,当波长1064 nm的基频光功率为1 W时,得到了功率为13.5 mW的532 nm连续倍频绿光输出,单通倍频转换效率为1.35%,归一化转换效率为1.69%/(W.cm),接近理论最大值。     

A geometric characterisation of resonance in Hopf bifurcation from relative equilibria

We give a new characterisation of resonance in Hopf bifurcation from relative equilibria in systems with compact symmetry group. This characterisation provides a full geometric explanation of the resonance phenomenon. In addition, we develop techniques based on normal form theory to give a complete solution to the associated bifurcation problem.     

Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation

Based on the computerized symbolic system Maple and a Riccati equation, a Riccati equation expansion method is presented by a general ansatz. Compared with most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear differential equations. Making use of the method, we study the Bogoyavlenskii's generalized breaking soliton equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions.     

利用集总L-C元件构造的一维metamaterials特性的实验研究

在普通微带传输线中周期性地加载集总L C元件能够构造一维特异性材料(metamaterials)，它具有与众不同的特异性质.通过实验证实了波在这种结构中传播具有相速度与群速度方向相反的左手性通带，其折射率为负值，并发现平均折射率为零的能隙.这种结构具有结构紧凑，参数可调，制作简单的优点. 关键词： 负折射率 特异性材料 周期性结构 微带线     

Remarks on the notion of mean free path for a periodic array of spherical obstacles

In this note, we explain in detail how the notion of mean free path is related to the mathematical results obtained in our previous paper.