一致分数阶非线性微分方程的精确解

同时考虑了Kudryashov方法和Khalil一致分数阶变换,构造了求解一致分数阶非线性微分方程精确解的新方法,并将其用于求解时间-空间一致分数阶Whitham-Boroer-Kaup方程,得到了Whitham-Boroer-Kaup方程新的精确解,验证了该方法的有效性和可行性.     

三角级数在Burgers-KdV混合型方程中的应用

利用三角级数法将Burgers-KdV混合型方程转化为一组非线性代数方程,进而用待定系数法求解方程组,最后求出了Burgers-KdV混合型方程的精确解.     

Adomian分解法求解非线性分数阶Fredholm积分微分方程

为了求解一类非线性分数阶Fredholm积分微分方程的数值解,本文将Adomian分解法(Adomian Decomposition Method,ADM)引入到非线性分数阶Fredholm微积分方程的求解中.将ADM多项式与分数阶积分定义有效结合,得到Adomian级数解.通过收敛性分析证明所得的级数解收敛于精确解,给出最大绝对截断误差.并结合实例,证明方法的有效性和实用性.     

分数阶广义扰动热波方程的与泛函映射解

研究了一类分数阶广义非线性扰动热波方程.首先在典型分数阶热波方程情形下得到解,接着用泛函分析映射方法,求出了分数阶广义非线性扰动热波方程初始边值问题的任意次近似解析解.最后简述了它的物理意义.求得的近似解析解,弥补了单纯用数值方法得到的模拟解的不足.     

一类高阶非线性波方程的子方程与精确行波解

结合子方程和动力系统分析的方法研究了一类五阶非线性波方程的精确行波解.得到了这类方程所蕴含的子方程, 并利用子方程在不同参数条件下的精确解, 给出了研究这类高阶非线性波方程行波解的方法, 并以Sawada Kotera方程为例, 给出了该方程的两组精确谷状孤波解和两组光滑周期波解.该研究方法适用于形如对应行波系统可以约化为只含有偶数阶导数、一阶导数平方和未知函数的多项式形式的高阶非线性波方程行波解的研究.     

长水波近似方程组的新精确解

依据齐次平衡法的思想 ,首先提出了求非线性发展方程精确解的新思路 ,这种方法通过改变待定函数的次序 ,优势是使求解的复杂计算得到简化 .应用本文的思路 ,可得到某些非线性偏微分方程的新解 .其次我们给出了长水波近似方程组的一些新精确解 ,其中包括椭圆周期解 ,我们推广了有关长波近似方程的已有结果 .     

一类非线性分数阶发展方程的新精确解

利用exp(-Φ(ξ)展开法,分别得到非线性分数阶Phi-4方程,非线性分数阶foam drainage方程,非线性分数阶SRLW方程的新精确解.实践证明,方法简洁方便,对于研究非线性分数阶发展方程具有十分重要的意义.     

首次积分法求时空-分数阶MkdV-ZK方程新的精确解

为了给物理学中的动力学行为研究提供依据,更好解释一些物理现象.首先使用分数阶复变换将时空-分数阶MKdV-ZK方程转换为非线性常微分方程组,其次使用除法定理寻求常微分方程组的首次积分,最后使用首次积分求解出原方程的许多精确解,得到了时空-分数阶MKdV-ZK方程的新精确解.数值结果表明首次积分法是有效的,该方法具有简单便捷等优点.     

非线性波方程的精确孤立波解

立了一种求解非线性波方程精确孤立波解的双曲函数方法,并在计算机代数系统上加以实现,推导出了一大批非线性波方程的精确孤立波解.方法的基本原理是利用非线性波方程孤立波解的局部性特点,将方程的孤立波解表示为双曲函数的多项式,从而将非线性波方程的求解问题转化为非线性代数方程组的求解问题.利用吴消元法或Gröbner基方法在计算机代数系统上求解非线性代数方程组, 最终获得非线性波方程的精确孤立波解,其中有很多新的精确孤立波解.     

分数阶及整数阶Klein-Gordon方程的孤立波解研究

Klein-Gordon方程是量子力学领域的一类重要方程,它是薛定谔方程的一种相对论形式,包括分数阶和整数阶方程,寻求它的解有着重要的意义.利用一种较为实用的1/G展开法,对一类分数阶Klein-Gordon方程和相应的整数阶Klein-Gordon方程进行了求解,得到了丰富的行波解,包括孤立波解和扭曲波解,同时有代表性地选择一些解,来画出它们的图形并进行相图分析.另外,对所得到的整数阶与分数阶方程的解进行了对比,发现了它们的异同点.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.