RWn^d的常返性

设X＝{X(z),z∈T^n}是文献[1]中定义的n参数d维随机游动（RWn^d)，本文主要研究RWn^d的常返性，得到了关于RWn^d的常返性的一些判别准则，并举例说明了几种RWn^d的常返性。     

RWdn的常返性

设X={X(z),z∈Tn}是文献[1]中定义的n参数d维随机游动(RWdn),本文主要研究RWdn的常返性,得到了关于RWdn的常返性的一些判别准则,并举例说明了几种RWdn的常返性.     

求一类常系数线性常微分方程特解的有限递推法

对于非齐次项为多项式,指数函数,正(余)弦函数,或它们的乘积形式的常系数线性常微分方程,提出了求其特解的有限递推法.它方法统一,计算简洁,便于编程,能解决高阶问题,能在有限步内得出方程的解析特解,因而优于目前广泛采用的待定系数法.     

有限链环上的常循环码

研究了有限链环R上常循环码的等价性,根据等价性给出了R上一些常循环码及其对偶码的结构.确定了该环上长度为ps的所有常循环码及其对偶码的结构.     

常系数线性齐次常微分方程解的级数表示

给出了常系数线性齐次常微分方程初值问题的解的Maclaurin级数的明显表达式.     

三类常系数非线性常微分方程的特解表达式

应用算子解法给出一类特殊类型的常系数非齐线性常微分方程的特解表达式,结合复数解法得到两类较为一般的常系数非齐线性常微分方程的特解表达式．     

关于一般马尔可夫过程轨道常返性及暂留性

本文讨论了一般马尔可夫过程轨道常返性及暂留性，得到了一般马尔可夫过程轨道点常返及区域常返的一些判别准则。     

用分部积分法求解常系数高阶非齐次线性常微分方程

众所周知 ,对于常系数高阶非齐次线性常微分方程y(n) + a1 y(n-1 ) +… + an-1 y′+ any=f( x) , ( 1)只要求出与 ( 1)相应的齐次线性常微分方程y(n) + a1 y(n-1 ) +… + an-1 y′+ any=0 ( 2 )的特征方程λn+ a1 λn-1 +… + an-1 λ+ an=0 ( 3)的特征根 λ1 ,λ2 ,… ,λs,它们的重数分别为 n1 ,n2 ,… ,ns ∑ ni=n ,此时 ,齐次线性常微分方程 ( 2 )的一个基本解组为eλ1x,xeλ1x,… ,xn1-1 eλ1x;… ;eλsx,xeλsx ,… ,xns-1 eλsx ,( 4)并且再求出非齐次线性常微分方程 ( 1)的一个特解 ,则我们就能求出非齐次方程 ( 1)的通解 .有许多方…     

常微分方程解题模式的构建

为了解决常微分方程教学实践中出现的“断点”问题．在Polya解题观和建构主义学习观的指导下,结合大学常微分方程知识特点,提出基于Polya解题观的常微分方程解题模式。实践表明,本模式对于提高常微分方程教学效果和学生的学习效率具有一定的理论和实践意义．     

求解常微分方程的凑微分法

介绍一些求解常微分方程的凑微分方法.     

Exact solutions of the Kudryashov-Sinelshchikov equation

The Kudryashov-Sinelshchikov equation for describing the pressure waves in liquid with gas bubbles is studied. New exact solutions of this equation are found. Modification of truncated expansion method is used for obtaining exact solution of this equation.     

一般区间上柱Bessel方程本征值问题特征问题根的Matlab算法

Root of characteristic equation for cylindrical Bessel equation eigenvalue prob-lems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.     

Approximate Solution of the Kuramoto-Shivashinsky Equation on an Unbounded Domain

The main goal of this paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded domain near a change of bifurcation, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation, which is called the Ginzburg-Landau (G-L for short) equation, for the amplitudes of the dominating modes.     

Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known twodimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 35–48, July, 2009.     

Navier-Stokes方程与Euler方程的稳定性比较

比较了Navier-Stokes 方程和Euler方程的稳定性;并以它们的典型初值问题为例,分析了Navier-Stokes方程和Euler方程稳定性不同的原因．     

Nonlocal Symmetries of the Camassa-Holm Type Equations

A class of nonlocal symmetries of the Camassa-Holm type equations with bi-Hamiltonian structures, including the Camassa-Holm equation, the modified Camassa-Holm equation, Novikov equation and Degasperis-Procesi equation, is studied. The nonlocal symmetries are derived by looking for the kernels of the recursion operators and their inverse operators of these equations. To find the kernels of the recursion operators, the authors adapt the known factorization results for the recursion operators of the KdV, modified KdV, Sawada-Kotera and Kaup-Kupershmidt hierarchies, and the explicit Liouville correspondences between the KdV and Camassa-Holm hierarchies, the modified KdV and modified Camassa-Holm hierarchies, the Novikov and Sawada-Kotera hierarchies, as well as the Degasperis-Procesi and Kaup-Kupershmidt hierarchies.     

New exact solutions for a generalization of the Korteweg-de Vries equation (KdV6)

The generalized tanh-coth method is used to construct periodic and soliton solutions for a new integrable system, which has been derived from an integrable sixth-order nonlinear wave equation (KdV6). The system is formed by two equations. One of the equations may be considered as a Korteweg-de Vries equation with a source and the second equation is a third-order linear differential equation.     

Comment on “New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”

In this comment we analyze the paper [Abdelhalim Ebaid, S.M. Khaled, New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity, J. Comput. Appl. Math. 235 (2011) 1984-1992]. Using the traveling wave, Ebaid and Khaled have found “new types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”. We demonstrate that the authors studied the well-known nonlinear ordinary differential equation with the well-known general solution. We illustrate that Ebaid and Khaled have looked for some exact solution for the reduction of the nonlinear Schrodinger equation taking the general solution of the same equation into account.     

一类非线性的偏微分方程的解

给出了一类带有时滞的偏微分方程.该方程描述得是含有非局部和时滞边界条件的分布参数系统.运用泛函分析和积分方程的理论,证明了方程解的存在唯一性,得到解的解析表达式.     

New traveling waves solutions to generalized Kaup-Kupershmidt and Ito equations

In this paper we consider a special fifth-order KdV equation with constant coefficients and we obtain traveling wave solutions for it, using the projective Riccati equation method. By mean of a scaling, exact solutions to general Kaup-Kupershmidt (KK) equation are obtained. As a particular case, exact solutions to standard KK equation can be derived. Using the same method, we obtain exact solutions to standard Ito equation. By mean of scaling, new exact solutions to general Ito equation are formally derived.