一类非线性演化方程新的显式行波解

借助Mathematica软件和吴方法,采用双曲函数法,获得了一类非线性演化方程u_tt+au_xx+bu+cu2+du3=0的多组行波解,其中包括周期解与孤子解.这种方法也适用于其他非线性方程或方程组.     

广义Pochhammer-Chree方程的显式精确孤波解

首先对广义Pochhammer-Chre方程(PC方程)u_tt-u_ttxx+ru_xxt-(a₁u+a₂u2+a₃u3)_xx=0(r≠0)(Ⅰ)的孤波解u(ξ)建立了公式∫_-∞+∞[u'(ξ)]2dξ=1/12rv(C₊-C_-)3[3a₃(C₊+C_-)+2a₂]。由此推知:广义PC方程(Ⅰ)不可能有钟状孤波解,只可能有扭状孤波解;而广义PC方程u_tt-u_ttxx-(a₁u+a₂u2+a₃u3)_xx=0(Ⅱ)可能既有钟状孤波解又有渐近值满足3a₃(C₊+C_-)+2a₂=0的扭状孤波解。进一步求出了广义PC方程(Ⅰ)的扭状孤波解,求出了广义PC方程(Ⅱ)的钟状孤波解和渐近值满足2a₃(C₊+C_-)+2a₂=0的扭状孤波解。最后给出了广义PC方程u_tt-u_ttxx-(a₁u+a₃u3+a₅u5)_xx=0(Ⅲ)的显式孤波解。     

获得非线性微分方程显式解析解的两种新算法

基于AC=BD的思想来求解非线性微分方程(组)。设Au=0为给定的待求解的方程,Dv=0是容易求解的方程。如果可以获得变换u=Cv使得v满足Dv=0,则能够得到Au=0的解。为了说明该种途径,本文举例给出几种变换C的表达式。     

一类半线性椭圆型方程衰减正整解的存在唯一性

本文首先证明方程△u-m2u+f(x,u)=0,x∈Rn,n≥3,m>0存在衰减的正整解,然后重点证明这种解的唯一性。     

非自治时滞微分方程的扰动全局吸引性*

考虑具有扰动项的非自治时滞微分方程x>(t)=-a(t)x(t-τ)+F(t,x_t),t≥0(*)其中F:[0,∞)×C[-δ,0]→R且连续,C[-δ,0]表示将[-δ,0]映射到R的所有连续函数集合.F(t,0)≡0,a(t)∈C((0,∞),(0,∞)),τ≥0.通常文献对a(t)不依赖于t即a(t)为自治情形,研究了方程(*)零解的局部或全局渐近性质[1～5,7].本文对a(t)为非自治即依赖于t之情形,获得了方程(*)零解全局吸引的充分条件,所得结论在某种意义上说是不可改进的.本文改进和推广了已有文献的相应结果,同时本文采用的方法可应用到非自治非线性扰动方程.     

一类高阶中立型方程的周期解

利用Fourier级数理论讨论了一类高阶中立型方程的周期解问题。所得结果改进了司建国(应用数学和力学,第17卷1期:关于高阶常系数中立型方程周期解的讨论)的主要结果,即将该文定理1的条件|b₀|<1/2改为|b₀|≠1,从而该文的其它定理也可相应得到改进。     

关于不可压、无粘流体的Euler方程初值问题的适定性(Ⅰ)

以分层理论为基础,讨论了Euler方程不适定的初值问题以及不适定问题的形式可解性,并给出了某些不适定初值问题存在形式解的条件与计算方法。特别讨论了R4中的超平面{t=0}上初值问题的适定性并给出了存在不唯一解的例证。     

扩展浅水波方程的精确相互作用解

将相容的双曲正切函数展开法(CTE方法)和截断Painlevé分析法应用于扩展浅水波方程,并通过这两个方法求解相容性方程的若干精确相互作用解,包括如孤子与周期波相互作用解、变振幅周期波与椭圆周期波相互作用解.     

三维抛物型方程的一族高精度分支稳定显格式

构造了一族解三维抛物型方程的高精度显格式,其稳定性条件为r=Δt/Δx2=Δt/Δy2=Δt/Δz2<1/2,截断误差为O(Δt2+Δx4).     

Maxwell方程的多余阶次与恰当解

设pu=f在Ω内对任意f有解,其中p是任意线性常系数偏微分算子.在本文中我们证明Maxwell方程相当于四阶方程,齐次Maxwell方程的一般解为 其中φ_i满足□φ_i=0 i=1.2.     

Fehlerabsehätzung beim verfahren von wolfe zur lösung quadratischer optimierungsproblem mit hilfe der intervallarithmetik

This paper is dealt with error estimations for solutions of quadratic programming problems. These estimations are given by solution of a linear system of equations by means of the methods of interval arithmetic. Therefore it is quite certain that the round off errors are also included in these estimations.     

Quasilinear iterative scheme for a fourth-order differential equation with retardation and anticipation

In this paper, the estimations of error between the approximate solution and the solution for a fourth-order differential equation with retardation and anticipation are given by employing the quasilinear iterative scheme and the approximate quasilinear iterative scheme.     

Statistical Analysis Technique of Two-parameter Generalized Exponential Sum Distribution

A new life distribution is proposed, known as ``two-parameter generalized exponential sum distribution". We study the density function and failure rate function, the average failure rate function, the image features and the numerical characteristics of the mean residual life of the distribution. Several methods of calculating point estimation of parameters are discussed. Through the Monte-Carlo simulation, we compare the precision of the point estimations. In our opinion, the best linear unbiased estimation is the most optimal solution of these methods. At the same time, several methods of calculating parameters of interval estimations are given. We also discuss the precision of interval estimations by Monte-Carlo simulation and use the best linear unbiased estimation and the best linear invariant estimation to construct interval estimations which are better than other estimation method. Finally, several simulation examples and a case of maintaining tanks is used to illustrate the application of the methods presented in this paper.     

Approximation in eigenvalue problems for holomorphic fredholm operator functions I

The approximation of a holomorphic eigenvalue problem is considered. The main purpose is to present a construction by which the derivation of the asymptotic error estimations for the approximate eigenvalues of Fredholm operator functions can be reduced to the derivation of these estimations for the case of matrix functions. (Some estimations for the latter problem can be derived, in one's turn, from the error estimations for the zeros of the corresponding determinants.) The asymptotic error estimations are considered in part II of this paper, in [10]. By the presented construction also the stability of the algebraic multiplicity of eigenvalues by regular approximation is proved in Section 3

The presented construction, in essence, reproduces the constructions in [7] for the case of the compact approximation in subspaces and in [9] for the case of projection—like methods. It is simpler to use than similiar construction in [8], and allows unified consideration of the general case and the case of projection—like methods, what in [8, 9] was not achieved     

二元算子方程组的迭代求解方法

利用锥理论和单调迭代方法,本文在Banach空间中对三类二元算子方程组的求解进行了探讨,利用较简捷的条件得出方程组的唯一解和迭代逼近式及误差估计式并推广到了n元算子方程组的情形,得到相应结果．     

Singularly Perturbed Solution of Three Species Volterra Model with Constant Harvest and Invest Rates

<正> In this paper, we consider the three species Volterra model of the first-order nonlinear differential equations. Using the method of multiple scales, the.asymptotic expansions of solution for the original problem are obtained, and the uniformly valid asymptotic estimations of the solution are discussed.     

The convergence of the horizontal line method for Maxwell's equations

The interior initial-boundary value problem for Maxwell's equations is considered for certain homogeneous boundary conditions and currents which satisfy corresponding compatibility conditions. Under the assumption that a solution exists, it is shown by means of suitable normed spaces that the sequence of discrete solutions obtained from the horizontal line method converges discretely to this solution. A priori estimations are given both for the discrete solutions and the solution of the given problem.     

Numerical Solution of the Reaction-Diffusion Equation

In this paper, we consider the numerical solution for the reaction-diffusion equation. A finite difference scheme and the basic error equality are given. Then the error estimations are proved for the periodic problem with $v(x,t)\geq 0$, the first and second boundary value problems with $v(x,t)\geq v_0＞0$, and for $v(U)\geq v_0›0$. Under some conditions such estimations imply the stabilities and convergences of the schemes.     

磁流体力学方程组的激波生成

研究磁流体横向流动的一维模型,在解的强间断出现后流场的性质。利用迭代法具体构造了该方程组的强间断—激波以及问题的熵解。同时,利用激波的性质,给出了各物理参量在爆破点附近的奇性估计。     

一类求解BURGERS方程的LEGENDRE谱格式

本文考虑非稳态Burgers方程的初边值问题,构造了一类Legendre谱计算格式,证明了其收敛性并给出了一些数值试验结果。