RLW—Burgers方程的精确解

借助未知函数的变换，ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程化为易于求解的齐次形式的方程，从而得到ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程的精确解。     

Glowinski区域分解算法的收敛性方程：Stokes方程

Ｇｌｏｗｉｎｓｋｉ区域分解算法的收敛性方程──Ｓｔｏｋｅｓ方程储德林，胡显承（清华大学应用数学系，北京１０００８４）ＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＧＬＯＷＩＮＳＫＩ＇ＳＤＯＭＡＩＮＤＥＣＯＭＰＯＳＩＴＩＯＮＡＬＧＯＲＩＴＨＭ──ＳＴＯＫＥＳＥＱＵＡ...     

组合KdT与MKdV方程的显式精确解

本文通过直接代数方法与假设方法的一种结合,求出了组合ＫｄＶ和ＭＫｄＶ方程的一些显式精确行波解。     

Burgers与组合KdV混合型方程的精确解

该文求出了组合ＫｄＶ方程的渐近值不为零的钟状孤波解和扭状孤波解；求出了Ｂｕｒｇｅｒｓ与组合ＫｄＶ混合型方程ｕｔ＋ａｕｕｘ＋ｂｕ２ｕｘ＋ｒｕ（ｘｘ）＋ｕ（ｘｘｘ）＝０的二类扭状孤波解．作为推论，还求出了波方程ｕ（ｔｔ）－ｋｕ（ｘｘ）＋ｐｕ十ｑｕ２＋ｓｕ３＝０的钟状和扭状孤波解．     

一类带有非均匀项的广义KdV方程的孤波解

一类带有非均匀项的广义ＫｄＶ方程的孤波解朱佐农（扬州大学农学院基础部，扬州２２５Ｏ０１）－、引言众所周知，ＫｄＶ方程已被广泛研究［１］．从方程（１）的高阶守恒量出发，Ｌａｘ得到第一族高阶ＫｄＶ方程，其５阶形式为：从（２）的守恒量出发，Ｓａｗａｄａ和Ｋ...     

KdV—KSV方程的初值问题

本文证明了ＫｄＶ－ＫＳＶ方程的周期边值问题和Ｃａｕｃｈｙ问题广义解和古典解的整体存在性，正则性及唯一性。     

非线性发展方程新的显式精确解

借助Ｍａｔｈｅｍａｔｉｃａ系统,采用三角函数法和吴文俊消元法,本文获得了著名的２＋１维ＫＰ方程的若干精确解,其中包括新的精确解和孤波解．在此基础上,进而得到著名ＫｄＶ方程、Ｈｉｒｏｔａ－Ｓａｔｓｕｍａ方程和耦合ＫｄＶ方程的一些精确解．     

组合KdV与MKdV方程的显式精确解

本文通过直接代数方法与假设方法的一种结合,求出了组合ＫｄＶ和ＭＫｄＶ方程的一些显式精确行波解．     

Burgers-KdV混合型方程的显式精确解

本文提出了双参数假设,用直接积分的方法得到了Ｂｕｒｇｅｒｓ－ＫｄＶ方程的显式精确解,分析了解的结构。     

可积的与Hamilton形式的NLS-MKdV方程族

本文基于ｌｏｏｐ代数Ａ２的一个特殊子代数，设计了一个等谱问题，应用屠规彰格式计算出一族具有Ｈａｍｉｌｔｏｎ结构的可积系．此族含有非线性Ｓｃｈｒｄｉｎｇｅｒ方程与修正的ＫｄＶ方程，称之为ＮＬＳ ＭＫｄＶ方程族     

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.     

The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces

In this paper, we study the limit behavior of self-similar solutions for the Complex Ginzburg-Landau (CGL) equation in the nonstandard function space E_{s,p}. We prove the uniform existence of the solutions for the CGL equation and its limit equation in E_{s,p}. Moreover we show that the self-similar solutions of CGL equation converge, globally in time, to those of its limit equation as the parameters tend to zero. Key Words Ginzburg-Landau equation; Schrödinger equation; self-similar solution; limit behavior.     

几种广义非线性发展方程的新解

本文研究了构造了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解的问题.利用三种辅助方程及其新解,获得了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解.这些解由双曲余割函数、双曲正切函数、双曲正割函数、双曲余切函数和余割函数组成.     

Travelling Wave Solutions for Generalized Fisher Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１，２］，ＡｒｏｎｓｏｎａｎｄＷｅｉｎｂｅｒｇｅｒｈａｖｅｓｔｕｄｉｅｄｓｙｓｔｅｍａｔｉｃｌｙｔｈｅｓｃａｌａｒｎｏｎｌｉｎｅａｒｄｉｆｆｕ－ｓｉｏｎｅｑｕａｔｉｏｎｉｎｏｎｅｓｐａｃｅｖａｒｉａｂｌｅｕｔ＝ｕｘｘ＋φ（ｕ），（１．１）ｗｈｅｒｅｕ＝ｕ（ｘ，ｔ）ａｎｄφ（ｕ）ｉｓａｎｏｎｌｉｎｅａｒｆｕｎｃｔｉｏｎ．Ｅｑｕａｔｉｏｎ（１．１）ａｒｉｓｅｓｉｎｓｅｖｅｒａｌａｐｐｌｉｃａ－ｔｉｏｎｓ；Ｓｅｅ［１，２］ａｎｄ［３］ｆｏｒｉｎｆｏｒｍａｔｉｏｎａ…     

差分方程x_(n 1)=x_ne~r·((1-ax_n)/(1-bx_n))的全局吸引性

本文讨论差分方程的全局吸引性．证明了当时，*是全局吸引的．     

特征值问题的应用简述

从矩阵的特征问题入手,引出常系数线性齐次微分方程求解的特征方程方法;利用分离变量法求解热传导方程,引入拉普拉斯方程的特征问题,给出求解过程,并给出热方程的解的渐近稳定性.     

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.     

A study on KdV and Gardner equations with time-dependent coefficients and forcing terms

In this work we study the KdV equation and the Gardner equation with time-dependent coefficients and forcing term for each equation. A generalized wave transformation is used to convert each equation to a homogeneous equation. The soliton ansatz will be applied to the homogeneous equations to obtain soliton solutions.     

关于双特征Beltrami方程

该文研究空间Ｂｅｌｔｒａｍｉ方程的推广形式，即双特征Ｂｅｌｔｒａｍｉ方程．利用外微分形式与矩阵的外代数等工具，将双特征Ｂｅｌｔｒａｍｉ方程转化为一个非齐次的狆 调和方程，转化过程中只用到加于特征矩阵的一致椭圆型条件．然后验证了算子犃满足的条件：Ｌｉｐｓｃｈｉｔｚ型条件、单调不等式、齐次性条件以及算子犅满足的控制增长条件．并利用得到的狆 调和方程，给出了双特征Ｂｅｌｔｒａｍｉ方程广义解分量函数的弱单调性结果．