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Exact traveling wave solutions and dynamical behavior for the (n+1)-dimensional multiple sine-Gordon equation

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science china mathematics 2007年第2期50卷 153-164页

作者： Ji-bin li department of mathematics, zhejiang normal university, jinhua 321004, china kunming university of science and technology, kunming 650093, china department of mathematics Zhejiang Normal University Jinhua China kunming university of science and technology Kunming China

Using the methods of dynamical systems for the (n+ 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions axe obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation exact explicit traveling wave solution double sine-Gordon equation multiple sine-Gordon equation.

Dynamical understanding of loop soliton solution for several nonlinear wave equations

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science china mathematics 2007年第6期50卷 773-785页

It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.

关键词： planar dynamical system homoclinic orbit solitary wave solution one-loop soliton solution periodic wave solution bifurcation nonlinear wave equation

Strong uniqueness of best approximations in spaces of bounded linear operators

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science china mathematics 2004年第3期47卷 339-351页

作者： li Chong HE Jinsu department of mathematics, zhejiang university Hangzhou 310027, china department of mathematics, zhejiang normal university jinhua 321004, china department of mathematics Zhejiang University Hangzhou China department of mathematics Zhejiang Normal University Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

TRAVEliNG WAVE SOLUTIONS FOR A CLASS OF NONliNEAR DISPERSIVE EQUATIONS

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Chinese Annals of mathematics,Series B 2002年第3期23卷 397-418页

作者： lijibin liUZHENGRONG CenterforNonlinearscienceStudies KunmingUniversityofScienceandTechnologyandInstituteofAppliedMathmaticsofYunnanProvinceKunming650093China. departmentofmathematics YunnanUniversityandInstituteofAppliedMathematicsofYunnanProvinceKunming650091China.

The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential *** using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are *** can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are *** different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.

关键词：行波解非线性扩散方程相平面孤波周期性偏微分方程分歧理论光滑性存在性参数可积系统跳跃

On the Cayley-Bacharach property and the construction of vector bundles

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science china mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2 1 department of mathematics and Statistics,Huazhong normal university,Wuhan 430079,china 2 department of mathematics,East china normal university,Shanghai 200241,china department of mathematics and Statistics Huazhong Normal University Wuhan China department of mathematics East China Normal University Shanghai China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词：向量丛财产 Cayley 射影余维自反

Taxonomic circumscription of Sinojackia xylocarpa (Styracaceae)

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Journal of Systematics and Evolution 2011年第2期49卷 163-164页

作者： 1 li-Qun LUO 2 Chi LUO 1 (department of Chemistry and life science, Leshan normal university, Leshan 614004, china) 2 (department of mathematics, Leshan normal university, Leshan 614004, china) (department of Chemistry and life science Leshan Normal University Leshan 614004 China) (department of mathematics Leshan Normal University Leshan 614004 China)

Sinojackia xylocarpa Hu in Journ. Arn. Arb. 9: 130. 1928. Type: china. Jiangsu: Nanjing, Y. L. Keng 1376 (PE!). Sinojackia rehderiana Hu in Journ. Arn. Arb. 11: 227. 1930, syn. nov. Type: china. Jiangxi: Nanchang, H. ... 详细信息

关键词： PE Styracaceae Taxonomic circumscription of Sinojackia xylocarpa

Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

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science china(Physics,Mechanics & Astronomy) 2008年第7期51卷 773-780页

作者： li lianHe1,2 & FAN TianYou1 1 department of Physics, Beijing Institute of technology, Beijing 100081, china 2 College of mathematics science, Inner Mongolia normal university, Hohhot 010022, china department of Physics Beijing Institute of Technology Beijing China College of mathematics science Inner Mongolia Normal University Hohhot China

The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.

关键词： icosahedral quasicrystals plane elasticity elliptic notch complex variable method

Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria

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science china mathematics 2012年第4期55卷 851-868页

作者： li Jun 1,& HUANG NanJing 2 1 College of mathematics and Information,china West normal university,Nanchong 637009,china 2 department of mathematics,Sichuan university,Chengdu 610064,china College of mathematics and Information China West Normal University Nanchong China department of mathematics Sichuan University Chengdu China

In this paper,the image space analysis (for short,ISA) is employed to investigate variational in- equalities (for short,VI) with cone *** separation for VI with cone constraints is characterized by using the normal cone to a regularization of the image,and saddle points of the generalized Lagrangian func- ***-type necessary and sufficient optimality conditions for VI with cone constraints are presented by using a separation *** functions and weak sharpness for VI with cone constraints are also investi- ***,the obtained results are applied to standard and time-dependent traffic equilibria introduced by Daniele,Maugeri and Oettli.

关键词：变分不等式空间分析交通应用拉格朗日函数图片分离定理时间依赖

Stability of a Neutral Stochastic Functional Differential Equations

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Wuhan university Journal of Natural sciences 2005年第6期10卷 957-960页

作者： li Bi-wen~1,21. department of mathematics, Hubei normal university, Huangshi 435002, Hubei, china 2. department of mathematics, Huazhong university of science and technology, Wuhan 430074, Hubei, china department of mathematics Hubei Normal University Huangshi Hubei China department of mathematics Huazhong University of Science and Technology Wuhan Hubei China

Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.

关键词： Lyapunov function D operator It's formula stochastic unifrom stabillty asymptotic stability