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Truncation Analysis for the Derivative Schrodinger Equation

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Acta Mathematica Sinica,English Series 2002年第1期18卷 137-146页

作者： XU Peng Cheng CHANG Qian Shun GUO Bo Ling Academy of Mathematics and System Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. China institute of applied physics and computational Mathematics. P. O. Box 8009. Beijing 100080. P. R. China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China institute of applied physics and computational Mathematics 8009 Beijing 10080 P. R. China

The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation the... 详细信息

关键词： Derivative nonlinear Schrodinger equation Geometric singular perturbation theory Melnikov's technique

求解二维三温能量方程的半粗化代数多重网格法

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数值计算与计算机应用 2003年第4期24卷 293-303页

作者：肖映雄舒适张平文莫则尧许进超湘潭大学计算与应用数学研究所湖南湘潭411105 北京大学数学科学学院北京100871 北京应用物理与计算数学研究所北京100088 美国宾州大学计算数学与应用研究中心

§1.引言二维三温辐射流体动力学方程组的求解是数值模拟的重要组成部分,而求解能量方程是一个十分重要的环节,而且在整个系统的计算中,能量方程求解所占的机时比重相当大(约80%以上).因此,寻求一个收敛快、稳定性好的二维三温能量方程... 详细信息

§1.引言二维三温辐射流体动力学方程组的求解是数值模拟的重要组成部分,而求解能量方程是一个十分重要的环节,而且在整个系统的计算中,能量方程求解所占的机时比重相当大(约80%以上).因此,寻求一个收敛快、稳定性好的二维三温能量方程数值解法是一个值得探讨的问题.二维三温能量方程可表示为非线性抛物型方程组,在二维柱对称Lagrange坐标系下,二维三温能量方程的标量式经简化得到如下方程组:

关键词：半粗化代数多重网格法二维三温能量方程流体动力学数值模拟抛物型方程组

A three-dimensional variational ocean data assimilation system:Scheme and preliminary results

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Science China Earth Sciences 2006年第11期49卷 1212-1222页

作者： ZHU Jiang1,2, ZHOU Guangqing1, YAN Changxiang1, FU Weiwei1 & YOU Xiaobao1,3 1. International center for Climate and Environment Sciences, institute of Atmospheric physics, Chinese Academy of Sciences, Beijing 100029, China 2. Jiangsu Key Laboratory of Meteorological Disaster, Nanjing University of Information Science and Technology, Nanjing 210044, China 3. Beijing institute of applied Meteorology, Beijing 100029, China 1. International center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China 2. Jiangsu Key Laboratory of Meteorological Disaster Nanjing University of Information Science and Technology Nanjing 210044 China 3. Beijing institute of applied Meteorology Beijing 100029 China

A new 3DVAR-based Ocean Variational Analysis System (OVALS) is developed. OVALS is capable of assimilating in situ sea water temperature and salinity observations and satellite altimetry data. As a component of OVALS, a new variational scheme is proposed to assimilate the sea surface height data. This scheme considers both the vertical correlation of background errors and the nonlinear temperature-salinity relationship which is derived from the generalization of the linear balance constraints to the nonlinear in the 3DVAR. By this scheme, the model temperature and salinity fields are directly adjusted from the altimetry data. Additionally, OVALS can assimilate the temperature and salinity profiles from the ARGO floats which have been implemented in recent years and some temperature and salinity data such as from expendable bathythermograph, moored ocean buoys, etc. A 21-year assimilation experiment is carried out by using OVALS and the Tropical Pacific circulation model. The results show that the assimilation system may effectively improve the estimations of temperature and salinity by assimilating all kinds of observations. Moreover, the root mean square errors of temperature and salinity in the upper depth less than 420 m reach 0.63℃ and 0.34 psu.

关键词： data assimilation, 3DVAR, sea surface height, ARGO floats.

On the Cauchy problem of generalized complex Ginzburg-Landau equation in three dimensions

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Progress in Natural Science:Materials International 2003年第9期 20-27页

作者： LI Donglong and GUO Boling (1. Guangxi institute of Technology, Liuzhou 545006, China 2. Graduate School of China Academy of Engineering physics, Beijing 100088, China 3. institute of applied physics and computational Mathematics, P. O. Box 8009, Beijing 100088, China) Guangxi institute of Technology，Liuzhou 545006，China Graduate School of China Academy of Engineering physics，Beijing 100088，China institute of applied physics and computational Mathematics，P. O. Box 8009，Beijing 100088，China

The generlized complex Ginzburg-Landau equation (CGL) under periodic boundary condition is studied. The existenceof global solution for this equation is established under appropriate assumption on a nonlinear σ, whic... 详细信息

关键词： generalized complex Ginzburg-Landau equation global solution.

Existence of the classical solution and almost periodic solution for the Camassa-Holm type equations

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Progress in Natural Science:Materials International 2004年第4期 17-22页

作者： YANG Ling'e and GUO Boling (1. Department of Mathematics, Foshan University, Foshan 528000, China 2. Graduate School, China Academy of Engineering physics, Bejing 100088, China 3. institute of applied physics and computational Mathematics, Beijing 100088, China) DepartmentofMathematics FoshanUniversityFoshan528000China instituteofappliedphysicsandcomputationalMathematics Beijing100088China

Using Banach fixed point theorem and a priori estimate, the existence of periodic and almost periodic solutions of Ca-massa-Holm type equation with a nonlinear boundary condition are respectively proved when g (x, t) ... 详细信息

关键词： Camassa-Holm equation almost periodic solution existence.

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非线性相干作用的动力学理论

红河学院学报 1989年第2期 1-20页

作者：贺贤土应用物理与计算数学研究所

本文求出了Vlasov方程的微扰解和三波共振方程的精确解,并研究了等离子体中的回声问题,建立了非线性相干作用的动力学理论。

关键词： Vlasov方程三波共振方程回声非线性相干作用

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自由电子激光中的混沌现象及控制

物理学进展 1995年第1期15卷 19-78页

作者：王文杰王光瑞陈式刚杜祥琬北京应用物理与计算数学研究所中国科学院国际材料物理中心

本文评述了高技术项目之一自由电子激光（下文中简记为ＦＥＬ）中的混沌问题。着重讨论了ＦＥＬ中电子运动和光场发展的不稳定性与混沌现象，以及电子相空间运动轨道的混沌与光场混沌的控制、利用等。在讨论过程中，利用了混沌理论研究... 详细信息

本文评述了高技术项目之一自由电子激光（下文中简记为ＦＥＬ）中的混沌问题。着重讨论了ＦＥＬ中电子运动和光场发展的不稳定性与混沌现象，以及电子相空间运动轨道的混沌与光场混沌的控制、利用等。在讨论过程中，利用了混沌理论研究中的一些典型方法，如作Ｐｏｉｎｃａｒｅ截面，画电子的相空间运动轨道，计算Ｌｉａ－ｐｕｎｏｖ指数，作功率谱等。从而揭示ＦＥＬ中各种稳定、不稳定、及混沌等现象的内在规律性。最后，针对探索ＦＥＬ的新概念、ＦＥＬ技术的发展等问题，本文提出了一些具体的建议。

关键词：自由电子激光混沌现象控制

高频波激发低频磁场和离子声波的重整化强湍动理论

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物理学报 1986年第3期 283-299页

作者：贺贤土应用物理与计算数学研究所北京

本文给出了高温等离子体中高频波激发低频磁场和离子声波强湍动过程的重整化理论,以便改善通常的弱非线性处理方法,从Vlasov-Maxwell方程组出发,在Fourier表象中得到了包含“最发散”和“次发散”效应互相耦合的高频和低频传播于重整化... 详细信息

本文给出了高温等离子体中高频波激发低频磁场和离子声波强湍动过程的重整化理论,以便改善通常的弱非线性处理方法,从Vlasov-Maxwell方程组出发,在Fourier表象中得到了包含“最发散”和“次发散”效应互相耦合的高频和低频传播于重整化方程组,从而获得了高、低频振荡粒子重整化分布函数和场的耦合关系。在“最发散”重整化近似下,我们求解了高低频传播子方程组,得到了展开到v4（高频湍动场能密度与等离子体热能密度之比）一次方的近似解和重整化介电函数等表达式。然后,在Fourier逆变换下导得了我们所要的时空表用中重整化强湍动方程组。最后,作为一个说明重整化作用的例子,在一维稳态下求解了孤立子的形式。

关键词：重整化强湍动群论离子声波传播子方程组联立方程低频磁场

Method of Green’s function of nonlinear vibration of corrugated shallow shells

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Science China(physics,Mechanics & Astronomy) 2008年第6期51卷 678-686页

作者： YUAN Hong Key Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of China, institute of applied Mechanics, Jinan University, Guangzhou 510632, China 1. Key Laboratory of Disaster Forecast and Control in Engineering Ministry of Education of China Institute of Applied Mechanics Jinan University Guangzhou 510632 China

Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations be-came nonlinear ordinary differential equations with regard to time. The ampli-tude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.

关键词： corrugated shells spherical shells Green’s function integral equation nonlinear vibration