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Search Results: 1 - 10 of 78897 matches for " 孙峪怀 "
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广义KDV方程的显示行波解
怀
四川师范大学学报(自然科学版) , 2001,
Abstract: 非线性演化方程,特别是广义KDV方程因其丰富的数学物理内含而备受人们关注,其精确解的研究在理论和应用上都有重要的意义.求出了广义KDV方程的显示精确解,同时给出了解成立的条件,其求解方法也适用于求解其它非线性演化方程更多还原
一种指数式等温方程
One New Isotherm Equation Expressed in Exp Form
 [PDF]

陈俊祥, 怀, 刘福生
Applied Physics (APP) , 2012, DOI: 10.12677/APP.2012.23015
Abstract:

本文对Bridgman物态方程作进一步研究,构建了一种新的等温方程,这种方程具有及简单的指数形式。用它处理数据和进行运算比现有其他形式的等温方程都容易得多;它不仅能直接拟合已知初始密度的单相压力区的实验数据,而且也能直接拟合未知初始密度的单相压力区的实验数据。
 Based on the analysis in Bridgman equation of state (EOS), a new isotherm EOS for solids has been constructed. This new EOS takes an exponential form which is very simple for data process than other forms of isotherm EOS for solids. It is not only suitable for the experiment data fitting for the phase which the initial density is known, but also for the phase which initial density is unknown.

修改的(G′/G)-展开方法与 Sharma-Tasso-Olver方程的行波解
马志民,怀
四川师范大学学报(自然科学版) , 2014,
Abstract: 构造行波解是研究非线性偏微分方程的一个重要分支.主要描述了使用修改的(G′/G)-展开法求解非线性偏微分方程的过程.借助符号计算系统Maple软件,将此方法应用在求解Sharma-Tasso-Olver方程中,获得了该方程的一些新的行波解,例如u1\,u2\,u4和u5.这些新的结果有助于理解Sharma-Tasso-Olver方程的物理意义.
一类强非线性系统的稳定极限环
怀,马岷兴
四川师范大学学报(自然科学版) , 1999,
Abstract: 采用轨线流量法对强非线性系统¨x+x=ε(-x3+12·x+3110x2·x-·x3)的极限环的存在性、稳定性作出了判定,并求出了稳定极限环的轨线方程更多还原
一个非线性耗散色散系统精确解的符号计算
怀,刘福生
四川师范大学学报(自然科学版) , 2004,
Abstract: 非线性耗散色散系统的代表是BURGERSKDV方程,因其丰富的数学物理内含而备受人们关注.采用双曲函数方法将非线性演化方程求解问题转化为非线性代数方程组,再利用吴文俊消元法(WR)和计算机代数系统求解非线性代数方程组,从而获得的非线性偏微分方程显示精确解,其求解方法也适用于求解其它非线性演化方程
(2+1)维广义浅水波方程的Backlund变换和新精确解的构建
怀,程才,柳绪伦,张健
四川师范大学学报(自然科学版) , 2015, DOI: 10.3969/j.issn.1001-8395.2015.03.002
Abstract: (2+1)维浅水波方程广泛应用于描绘大气、河流、大海中的非线性现象.通过扩展的齐次平衡法研究了(2+1)维广义浅水波方程,得出了方程的Backlund变换、色散关系以及新的孤波解.该方法还可应用于处理其他高维浅水波方程.
非线性Chaffee-Infante反应扩散方程的新精确解
怀,杨少华,王佼,刘福生
四川师范大学学报(自然科学版) , 2012,
Abstract: 反应扩散方程描述了物质的输运、扩散和流动等物理过程,其精确解的构建在数学、物理、化学、生物等领域有其重要的应用意义.运用广义的Riccati方程代换法解Chaffee-Infante反应扩散方程,获得了27种形式的解,丰富了精确行波解的形式.推广运用该方法,可以构建其它类型的非线性反应扩散方程的行波解.
(3+1)维时空分数阶偏微分方程mKdV-ZK方程的新精确解
New exact solutions for the (3+1)-dimensional space-time fractional mKdV-ZK equation

洪韵,怀,江林,张雪
- , 2017,
Abstract: (3+1)维时空分数阶偏微分方程mKdV-ZK方程精确解的构建重要而令人感兴趣.本文通过含三维空间、一维时间的分数阶复变换将分数阶mKdV-ZK 方程转化为非线性常微分方程,再引入新的辅助微分方程的解及其新的展开形式,构建了mKdV-ZK方程系列精确解.
It is very important and interesting to construct the exact solutions of the (3+1)-dimensional space-time fractional mKdV-ZK equation.Firstly, by using fractional complex transformation, mKdV-ZK equation was transformed into a nonlinear ordinary deferential equation, and then introducing extends (G'/G)-expansion method to construct the exact solution. A series of new exact solution for mKdV-ZK equations have been obtained
空时分数阶mBBM方程的新精确解
New explicit solutions for the space-time fractional mBBM equation

康丽,怀,廖红梅,熊淑雪
- , 2018,
Abstract: 为了构造时空分数阶mBBM方程的新显式解, 本文首先利用分数阶复变换技巧将分数偏微分方程转化为常微分方程, 然后应用扩展的(G'/G)-展开法求解该常微分方程. 新精确解包括分别带有负幂次项的三角函数解, 双曲函数解及有理函数解.
In order to construct new explicit solutions of the space-time fractional mBBM equation, the fractional complex transformation is applied to turn the fractional partial differential equation into an ordinary differential equation (ODE). Then the extended (G'/G)-expansion method is used to solve the ODE. The new exact solutions contain trigonometric function solutions, hyperbolic function solutions, and rational functions with negative power exponent
几种广义的函数展开法在构建偏微分方程精确解中的文献综述与应用(G/G2)-展开法、(exp)-展开法构建(2 + 1)维Boiti-Leon-Pempinelli方程精确解
A Literature Review and Application of Sev Eral Generalized Function Expansion Methods in Constructing Exact Solutions of Partial Differential Equations(G/G2)-Expansion Method,(exp)-Expansion Method Construction (2 + 1) Exact Solution of the Dimensional Boiti-Leon-Pempinelli Equation
 [PDF]

吴大山, 怀, 杜玲禧
Advances in Applied Mathematics (AAM) , 2019, DOI: 10.12677/AAM.2019.810196
Abstract:
首先,系统给出(G/G2)-展开法、F-展开法、(exp)-展开法、改进的Kudryashov方法、直接截断法,构建偏微分方程的精确解的起源与研究现状的文献综述。接下来,采用对比方式给出上述五种广义的函数展开法在构建偏微分方程精确解的步骤。最后,通过上述五种广义的函数展开法中的(G/G2)-展开法、(exp)-展开法构建(2 + 1)维Boiti-Leon-Pempinelli方程的精确解,并使用控制变量法进行数学实验分析了(2 + 1)维Boiti-Leon-Pempinelli方程中三个变量对于精确解的影响。
First, the system gives(G/G2)-expansion method, F-expansion method, (exp)-expansion method, improved Kudryashov method, direct truncation method, to construct the literature review of the origin and research status of the exact solutions of partial differential equations. Next, the steps of constructing the exact solutions of the partial differential equations by the above five generalized function expansion methods are given in comparison. Finally, through the above five generalized (G/G2)-expansion method, (exp)-expansion method in the function expansion method constructs the exact solution of the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. The control variable method is used to analyze the influence of three variables on the exact solution in the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation.
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