期刊文献+
共找到46篇文章
< 1 2 3 >
每页显示 20 50 100
A Generalized Hirota Ansatz to Obtain Soliton-Like Solutions for a (3+l)-Dimensional Nonlinear Evolution Equation 被引量:1
1
作者 吴建平 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第8期297-300,共4页
Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theres... Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived. 展开更多
关键词 (3+1)-dimensional nonlinear evolution equation bilinear method generalized Hirota ansatz exponential type functions soliton-like solutions
下载PDF
A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation 被引量:2
2
作者 Panfeng Zheng Man Jia 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第12期147-156,共10页
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ... In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution. 展开更多
关键词 a reduced(3 + 1)-dimensional nonlinear evolution equation more general form of lump solution soliton induced by lump lumpoff and instanton/rogue wave solutions
下载PDF
New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov-Kuzentsov equation 被引量:14
3
作者 套格图桑 斯仁道尔吉 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第6期1143-1148,共6页
In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzent... In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term. 展开更多
关键词 generalized mKdV equation generalized Zakharov-Kuzentsov equation nonlinear evolution equation auxiliary equation exact solitary wave solutions
下载PDF
Extension of Variable Separable Solutions for Nonlinear Evolution Equations 被引量:3
4
作者 ZHANG Shun-Li ZHU Xiao-Ning +1 位作者 WANG Yong-Mao LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第4期829-832,共4页
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional sep... We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations. 展开更多
关键词 nonlinear evolution equation variable separable solution generalized conditional symmetry
下载PDF
Approximate Generalized Conditional Symmetries for Perturbed Evolution Equations 被引量:3
5
作者 ZHANG Shun-Li WANG Yong LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第6期975-980,共6页
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via th... The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples. 展开更多
关键词 perturbed evolution equation approximate generalized conditional symmetry approximate con ditional invariant solution
下载PDF
Variable Separation for(1+1)-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives 被引量:1
6
作者 WANG Peng-Zhou ZHANG Shun-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期797-802,共6页
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations withmixed partial derivatives.As an application,we classify equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admits de... We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations withmixed partial derivatives.As an application,we classify equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples. 展开更多
关键词 (1 1)-dimensional nonlinear evolution equations variable separation generalized conditional symmetry derivative-dependent functional separable solution
下载PDF
Solitary wave solutions for the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation
7
作者 Aly R.Seadawy Dianchen Lu Mostafa M.A.Khater 《Journal of Ocean Engineering and Science》 SCIE 2017年第2期137-142,共6页
In this paper,we utilize the exp(−ϕ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation.The generalized Zakharov-Kuzn... In this paper,we utilize the exp(−ϕ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation.The generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative impact.This model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma,liquids,acoustic waves in harmonic crystals and acoustic-gravity waves in compressible fluids.By using this method,seven different kinds of traveling wave solutions are successfully obtained for this model.The considered method and transformation techniques are efficient and consistent for solving nonlinear evolution equations and obtain exact solutions that are applied to the science and engineering fields. 展开更多
关键词 The exp(−ϕ(ξ))-expansion method The generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation Traveling wave solutions Solitary wave solutions
原文传递
含多维随机变量的广义概率密度演化方程解析解:以Euler-Bernoulli梁为例
8
作者 周永峰 李杰 《力学学报》 EI CAS CSCD 北大核心 2024年第9期2659-2668,共10页
广义概率密度演化方程的解析解,不仅具有重要理论价值,而且具有校验数值解、进而标定数值算法误差的作用.以Euler-Bernoulli简支梁为例,推导给出了梁受迫振动时跨中位移响应所对应的广义概率密度演化方程解析解.包括非平稳非高斯随机载... 广义概率密度演化方程的解析解,不仅具有重要理论价值,而且具有校验数值解、进而标定数值算法误差的作用.以Euler-Bernoulli简支梁为例,推导给出了梁受迫振动时跨中位移响应所对应的广义概率密度演化方程解析解.包括非平稳非高斯随机载荷作用下的解(包含2维随机变量)以及同时考虑载荷随机性和结构参数随机性时的解(分别包含2维、4维和5维随机变量).分析结果表明,真实的概率密度演化是一个十分复杂的过程,远不能用简单的概率分布函数加以描述.这一进展,可为概率密度演化理论的进一步深入研究提供一个方面的基础. 展开更多
关键词 广义概率密度演化方程 解析解 Euler-Bernoulli 受迫振动 多维随机变量
下载PDF
(3+1)维广义非线性发展方程的双线性Backlund变换与精确解
9
作者 薛宇英 套格图桑 《内蒙古师范大学学报(自然科学版)》 CAS 2024年第2期173-182,共10页
基于Hirota双线性方法和试探函数法,研究一个(3+1)维广义非线性发展方程的双线性Backlund变换和精确解问题。用Hirota双线性法,构造(3+1)维广义非线性发展方程的双线性形式和双线性Backlund变换。基于双线性形式和双线性Backlund变换,... 基于Hirota双线性方法和试探函数法,研究一个(3+1)维广义非线性发展方程的双线性Backlund变换和精确解问题。用Hirota双线性法,构造(3+1)维广义非线性发展方程的双线性形式和双线性Backlund变换。基于双线性形式和双线性Backlund变换,利用试探函数法与符号计算系统Mathematica,获得(3+1)维广义非线性发展方程的多种精确解,包括呼吸波解、复合型解、Lump周期解和孤子解,并分析解的相互作用情况。 展开更多
关键词 (3+1)维广义非线性发展方程 HIROTA双线性方法 BACKLUND变换 试探函数法 精确解
下载PDF
Lump and new interaction solutions to the (3+1)-dimensional nonlinear evolution equation
10
作者 Asma Issasfa Ji Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第12期25-34,共10页
In this paper,a new(3+1)-dimensional nonlinear evolution equation is introduced,through the generalized bilinear operators based on prime number p=3.By Maple symbolic calculation,one-,two-lump,and breather-type period... In this paper,a new(3+1)-dimensional nonlinear evolution equation is introduced,through the generalized bilinear operators based on prime number p=3.By Maple symbolic calculation,one-,two-lump,and breather-type periodic soliton solutions are obtained,where the condition of positiveness and analyticity of the lump solution are considered.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and breather-type periodic soliton are derived,by combining multi-exponential function or trigonometric sine and cosine functions with a quadratic one.In addition,new interaction solutions between a lump,periodic-solitary waves,and one-,two-or even three-kink solitons are constructed by using the ansatz technique.Finally,the characteristics of these various solutions are exhibited and illustrated graphically. 展开更多
关键词 generalized(3+1)-dimensional nonlinear evolution equation lump solution breather-type periodic soliton interaction solution generalized bilinear form
原文传递
A study on the compatibility of the generalized Kudryashov method to determine wave solutions
11
作者 Hemonta Kumar Barman Md.Ekramul Islam M.Ali Akbar 《Propulsion and Power Research》 SCIE 2021年第1期95-105,共11页
In this article,we establish solitary wave solutions to the Estevez-MansfieldClarkson(EMC)equation and the coupled sine-Gordon equations which are model equations to analyze the formation of shapes in liquid drops,su... In this article,we establish solitary wave solutions to the Estevez-MansfieldClarkson(EMC)equation and the coupled sine-Gordon equations which are model equations to analyze the formation of shapes in liquid drops,surfaces of negative constant curvature,etc.through contriving the generalized Kudryashov method.The extracted results introduce several types’solitary waves,such as the kink soliton,bell-shape soliton,compacton,singular soliton,peakon and other sort of soliton for distinct valuation of the unknown parameters.The achieved analytic solutions are interpreted in details and their 2D and 3D graphs are sketched.The obtained solutions and the physical structures explain the soliton phenomenon and reproduce the dynamic properties of the front of the travelling wave deformation generated in the dispersive media.It shows that the generalized Kudryashov method is powerful,compatible and might be used in further works to found novel solutions for other types of nonlinear evolution equations ascending in physical science and engineering. 展开更多
关键词 The nonlinear evolution equations(NLEEs) The Estevez-MansfieldClarkson(EMC)equation The coupled sineGordon equations The generalized Kudryashov method Solitons Analytic solutions
原文传递
广义Pochhammer-Chree方程的显式精确孤波解 被引量:14
12
作者 张卫国 马文秀 《应用数学和力学》 CSCD 北大核心 1999年第6期625-632,共8页
首先对广义Pochhammer_Chre方程(PC方程)ut-utxx+ruxxt-(a1u+a2u2+a3u3)xx=0(r≠0)(Ⅰ)的孤波解u(ξ)建立了公式∫+∞-∞[u′(ξ)]2dξ=112rv(C+-C... 首先对广义Pochhammer_Chre方程(PC方程)ut-utxx+ruxxt-(a1u+a2u2+a3u3)xx=0(r≠0)(Ⅰ)的孤波解u(ξ)建立了公式∫+∞-∞[u′(ξ)]2dξ=112rv(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ut-utxx-(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。 展开更多
关键词 非线性发展方程 广义 孤波解 精确解 P-C方程
下载PDF
利用(G'/G)展开法求解广义变系数Burgers方程 被引量:18
13
作者 庞晶 靳玲花 应孝梅 《量子电子学报》 CAS CSCD 北大核心 2011年第6期674-681,共8页
近年来,变系数非线性发展方程受到越来越多的关注。2008年王明亮等提出了一种新的方法,即(G′/G)展开法。将(G′/G)展开法首次尝试应用到变系数非线性发展方程中,并以广义变系数Burgers方程为例,成功得到了在系数满足一定条件时新的精确... 近年来,变系数非线性发展方程受到越来越多的关注。2008年王明亮等提出了一种新的方法,即(G′/G)展开法。将(G′/G)展开法首次尝试应用到变系数非线性发展方程中,并以广义变系数Burgers方程为例,成功得到了在系数满足一定条件时新的精确解;又尝试将该展开法进行新的扩展,再一次对广义变系数Burgers方程求解,又成功得到了一些新解。实践证明,该展开法不仅易于求解常系数非线性发展方程,而且对变系数非线性发展方程仍很高效、简洁、实用,并且具有广泛的应用前景。 展开更多
关键词 非线性发展方程 精确解 (G’/G)展开法 广义变系数Burgers方程
下载PDF
广义Hirota-Satsuma耦合KdV方程的精确解 被引量:9
14
作者 刘倩 周钰谦 刘合春 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2011年第3期335-339,共5页
利用(G'/G)-展开法结合数学软件Maple求得了广义Hirota-Satsuma耦合KdV方程的新精确解,包括孤波解、三角函数周期解和有理解.为了更直观地理解这些解,给出了它们的数值模拟图.
关键词 精确解 广义Hirota-Satsuma耦合KdV方程 (G'/G)-展开法 非线性发展方程
下载PDF
一类五阶非线性演化方程的广义孤立波解和周期解 被引量:5
15
作者 刘常福 戴正德 《西南大学学报(自然科学版)》 CAS CSCD 北大核心 2010年第1期1-4,共4页
应用指数函数法,借助计算机代数系统获得了包括五阶KdV方程、Sawada-Kotera方程和Kaup-Kupershmit方程在内的一类五阶非线性演化方程的广义孤立波解和周期解.结果表明,指数函数法结合符号计算已成为解决数学物理中非线性演化方程的强有... 应用指数函数法,借助计算机代数系统获得了包括五阶KdV方程、Sawada-Kotera方程和Kaup-Kupershmit方程在内的一类五阶非线性演化方程的广义孤立波解和周期解.结果表明,指数函数法结合符号计算已成为解决数学物理中非线性演化方程的强有力工具. 展开更多
关键词 五阶非线性演化方程 指数函数法 广义孤立波解 周期解
下载PDF
广义密度演化方程的δ函数序列解法 被引量:8
16
作者 范文亮 李杰 《力学学报》 EI CSCD 北大核心 2009年第3期398-409,共12页
随机动力系统响应或状态向量的概率密度函数一般遵循概率密度演化方程,如Liouville方程、FPK方程和Dostupov-Pugachev方程,但是上述方程均属于高维偏微分方程,求解相当困难.基于概率守恒原理的随机事件描述导出的广义密度演化方程,其维... 随机动力系统响应或状态向量的概率密度函数一般遵循概率密度演化方程,如Liouville方程、FPK方程和Dostupov-Pugachev方程,但是上述方程均属于高维偏微分方程,求解相当困难.基于概率守恒原理的随机事件描述导出的广义密度演化方程,其维数与系统自由度无关,为随机动力系统分析提供了可能的途径.从广义密度演化方程的形式解出发,引入δ函数的渐近序列,获得了广义密度演化方程的一种新的数值解法——广义密度演化方程的δ序列解法.将建议方法与非参数密度估计进行了对比,指出非参数密度估计是该方法的一个特例.最后,分别采用重构实例和演化实例验证了该方法在一维和多维情形下的有效性. 展开更多
关键词 概率守恒原理 广义密度演化方程 形式解 δ函数序列 非参数密度估计
下载PDF
四阶非线性发展方程的精确解和广义条件对称 被引量:5
17
作者 郑群珍 姬利娜 《纯粹数学与应用数学》 CSCD 北大核心 2007年第3期402-405,408,共5页
讨论了允许二阶广义条件对称的四阶非线性发展方程.通过广义条件对称方法得到了其对称约化和精确解.
关键词 广义条件对称 四阶非线性发展方程 对称约化 精确解
下载PDF
广义变系数Burgers方程的显示精确解 被引量:2
18
作者 邢秀芝 吴景珠 《河南大学学报(自然科学版)》 CAS 北大核心 2011年第6期562-566,共5页
将Riccati方程法扩展并应用到构造变系数非线性发展方程的显示精确解,发展了Riccati方程法,并用该方法获得了广义变系数Burgers方程在一定条件下的显示精确解.
关键词 非线性发展方程 投影Riccati方程法 广义变系数Burgers方程 显示精确解
下载PDF
变形Boussinesq方程组Ⅱ的推广解 被引量:1
19
作者 靳玲花 庞晶 《量子电子学报》 CAS CSCD 北大核心 2015年第4期425-430,共6页
为适应包括变系数方程在内的非线性发展方程求解的需要,试图探求辅助方程的多样化和解的形式的更为一般化,对王明亮提出的(G'/G)-展开法进行了更有意义的推广。为验证此推广的有效性,将它应用到常系数变形Boussinesq方程组Ⅱ中,取... 为适应包括变系数方程在内的非线性发展方程求解的需要,试图探求辅助方程的多样化和解的形式的更为一般化,对王明亮提出的(G'/G)-展开法进行了更有意义的推广。为验证此推广的有效性,将它应用到常系数变形Boussinesq方程组Ⅱ中,取得了多组精确行波解。实践证明此推广具有很好的适用性。 展开更多
关键词 非线性发展方程 精确解 推广的(G'/G)-展开法 变形Boussinesq方程组Ⅱ
下载PDF
一些非线性发展方程的显式行波解 被引量:4
20
作者 刘春平 《数学物理学报(A辑)》 CSCD 北大核心 2004年第6期661-668,共8页
该文给出了一种构造非线性发展方程显式行波解的方法 ,并用该方法得到了 Hirota-Satsuma方程组 ,一类非线性常微分方程以及广义耦合标量场方程组的显式行波解 .
关键词 行波解 非线性发展方程 Hirota-Satsuma方程组 广义耦合标量场方程组
下载PDF
上一页 1 2 3 下一页 到第
使用帮助 返回顶部