期刊文献+
共找到38篇文章
< 1 2 >
每页显示 20 50 100
A DIRECT APPROACH TO THE SOLITON PERTURBATION FOR KdV-MKdV EQUATION
1
作者 潘留仙 颜家壬 周光辉 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期356-360,共5页
The authors develop a direct approach to the soliton perturbation based on the separation of variables. With the aid of approach, the first-order effects of perturbation on a KdV-MKdV soliton are derived, both the slo... The authors develop a direct approach to the soliton perturbation based on the separation of variables. With the aid of approach, the first-order effects of perturbation on a KdV-MKdV soliton are derived, both the slow time-dependence of the soliton parameters and the first-order correction are obtained. 展开更多
关键词 KdV-MKdV equation soliton perturbation
下载PDF
Exact Topological Soliton Solutions to the Strongly Perturbed Family of Sine-Gordon Type Equations
2
作者 Stephen Johnson Essaid Zerrad +1 位作者 Sokratis Makrogiannis Jun Ren 《Journal of Applied Mathematics and Physics》 2019年第10期2401-2422,共22页
This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dis... This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dispersive and highly dispersive variations. After these solutions are found, strong perturbations are added to each equation and the new solutions are found. In solving both the perturbed and unperturbed sine-Gordon type equations, constraints are imposed on the parameters. The novel contributions of the authors are the soliton solutions to the strongly perturbed sine-Gordon equation and its variations. These results are important to the study of Josephson junctions, crystal dislocations, ultra-short optical pulses, relativistic field theory, and elementary particles. 展开更多
关键词 TOPOLOGICAL soliton KINK soliton SINE-GORDON equation Dispersion perturbation
下载PDF
Green's Function Method for Perturbed sine-Gordon Equation 被引量:1
3
作者 LIUFeng-Ming CAIHao LIUZheng-You HUANGNian-Ning 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期907-910,共4页
The usual Green's function method is introduced to show the completeness of the squared Jost solutions of the multi-soliton case in this work. Since sine-Gordon equation contains second derivative in time, the kno... The usual Green's function method is introduced to show the completeness of the squared Jost solutions of the multi-soliton case in this work. Since sine-Gordon equation contains second derivative in time, the known procedure with generalized Marchenko equation to show completeness relation of the eigenfunctions of linearized equation is unavailable. And the explicit expressions of Jost solutions are not necessary here. Thus a general method of direct perturbation method for the perturbed sine-Gordon equation is developed. 展开更多
关键词 solitonS nonlinear equation perturbation
下载PDF
N-Rotating Loop-Soliton Solution of the Coupled Integrable Dispersionless Equation
4
作者 Souleymanou Abbagari Saliou Youssoufa +3 位作者 Hermann T. Tchokouansi Victor K. Kuetche Thomas B. Bouetou Timoleon C. Kofane 《Journal of Applied Mathematics and Physics》 2017年第6期1370-1379,共10页
In this paper, we investigate the Rotating N Loop-Soliton solution of the coupled integrable dispersionless equation (CIDE) that describes a current-fed string within an external magnetic field in 2D-space. Through a ... In this paper, we investigate the Rotating N Loop-Soliton solution of the coupled integrable dispersionless equation (CIDE) that describes a current-fed string within an external magnetic field in 2D-space. Through a set of independent variable transformation, we derive the bilinear form of the CIDE Equation. Based on the Hirota’s method, Perturbation technique and Symbolic computation, we present the analytic N-rotating loop soliton solution and proceed to some illustrations by presenting the cases of three- and four-soliton solutions. 展开更多
关键词 COUPLED INTEGRABLE Dispersionless equation BILINEAR Method soliton Solutions perturbation Technique Symbolic Computation
下载PDF
On the analytical soliton approximations to fractional forced Korteweg-de Vries equation arising in fluids and plasmas using two novel techniques
5
作者 Weaam Alhejaili Emad A Az-Zo’bi +1 位作者 Rasool Shah S A El-Tantawy 《Communications in Theoretical Physics》 SCIE CAS CSCD 2024年第8期1-10,共10页
The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other asso... The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes. 展开更多
关键词 forced fractional KdV equation Caputo operator Yang homotopy perturbation method Yang transform decomposition method solitonS
原文传递
Landou-Ginburg-Higgs方程的微扰理论
6
作者 潘留仙 刘天贵 颜家壬 《湘潭大学自然科学学报》 CAS CSCD 2001年第1期25-29,共5页
研究了一阶近似下微扰对Landou -Ginburg -Higgs方程孤子解的影响 ,即求出了孤子参数随时间的缓慢变化关系及解的一阶修正的具体表达式 .
关键词 landou-ginburg-higgs方程 微扰理论 孤子解 分离变量法 物理学方程
下载PDF
Solitary Wave Solutions and Rational Solutions for Modified Zakharov-Kuznetsov Equation with Initial Value Problem 被引量:1
7
作者 Zhongzhou Dong Ling Wang 《Journal of Applied Mathematics and Physics》 2018年第5期949-959,共11页
The modified Zakharov-Kuznetsov equation with the initial value problem is studied numerically by means of homotopy perturbation method. The analytical approximate solutions of the modified Zakharov-Kuznetsov equation... The modified Zakharov-Kuznetsov equation with the initial value problem is studied numerically by means of homotopy perturbation method. The analytical approximate solutions of the modified Zakharov-Kuznetsov equation are obtained. Choosing the form of the initial value, the single solitary wave, two solitary waves and rational solutions are presented, some of which are shown by the plots. 展开更多
关键词 MODIFIED Zakharov-Kuznetsov equation HOMOTOPY perturbation Method soliton Solution
下载PDF
New Optical Soliton Solutions of the Perturbed Fokas-Lenells Equation 被引量:2
8
作者 Maha S.M.Shehata Hadi Rezazadeh +2 位作者 Emad H.M.Zahran Eric Tala-Tebue Ahmet Bekir 《Communications in Theoretical Physics》 SCIE CAS CSCD 2019年第11期1275-1280,共6页
In this article, we employ the perturbed Fokas-Lenells equation(FLE), which represents recent electronic communications. The Riccati-Bernoulli Sub-ODE method which does not depend on the balance rule is used for thefi... In this article, we employ the perturbed Fokas-Lenells equation(FLE), which represents recent electronic communications. The Riccati-Bernoulli Sub-ODE method which does not depend on the balance rule is used for thefirst time to obtain the new exact and solitary wave solutions of this equation. This technique is direct, effective and reduces the large volume of calculations. 展开更多
关键词 perturbED Fokas-Lenells equation(FLE) Riccati-Bernoulli Sub-ODE method optical soliton SOLUTIONS
原文传递
Analysis of the seventh-order Caputo fractional KdV equation:applications to the Sawada-Kotera-Ito and Lax equations
9
作者 Shabir Ahmad Sayed Saifullah 《Communications in Theoretical Physics》 SCIE CAS CSCD 2023年第8期14-24,共11页
In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementi... In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementioned fractional operator.The proposed approach combines the homotopy perturbation method(HPM)and the ZZ-transform.We consider two specific examples with suitable initial conditions and find the series solution to test their applicability.To demonstrate the utility of the presented technique,we explore its applications to the fractional Sawada–Kotera–Ito problem and the Lax equation.We observe the impact of a few fractional orders on the wave solution evolution for the problems under consideration.We provide the efficiency and reliability of the ZZHPM by calculating the absolute error between the series solution and the exact solution of both the Sawada–Kotera–Ito and Lax equations.The convergence and uniqueness of the solution are portrayed via fixed-point theory. 展开更多
关键词 seventh-order KdV equation soliton homotopy perturbation method
原文传递
变系数(2+1)维Sawada-Kotera方程的多孤子解
10
作者 耿勇 张金玉 +2 位作者 王丹 李春晖 王晓丽 《齐鲁工业大学学报》 CAS 2023年第2期19-25,共7页
借助Bell多项式和Hirota双线性算子理论,研究变系数(2+1)维Sawada-Kotera方程的多孤子解。首先介绍Bell多项式和Hirota双线性算子的基本理论,然后借助二者之间的关系详细推导出变系数(2+1)维Sawada-Kotera方程的双线性形式,再用摄动法... 借助Bell多项式和Hirota双线性算子理论,研究变系数(2+1)维Sawada-Kotera方程的多孤子解。首先介绍Bell多项式和Hirota双线性算子的基本理论,然后借助二者之间的关系详细推导出变系数(2+1)维Sawada-Kotera方程的双线性形式,再用摄动法对双线性形式进行求解得到其多孤子解,最后分析多孤子图像。 展开更多
关键词 Sawada-kotara方程 BELL多项式 Hirota双线性算子 摄动法 孤子解
下载PDF
EVOLUTION EQUATION OF OPTICAL SOLITONS IN FEMTOSECOND REGIME
11
作者 郭旗 周国生 +3 位作者 林为干 刘颂豪 廖常俊 金怀诚 《Science China Mathematics》 SCIE 1991年第11期1365-1377,共13页
A modified nonlinear Schrodinger equation (MNLSE), which is defined as the equationobtained by putting some higher-order terms (the higher-order dispersion and nonlinearity)into a nonlinear Schrodinger equation (NLSE)... A modified nonlinear Schrodinger equation (MNLSE), which is defined as the equationobtained by putting some higher-order terms (the higher-order dispersion and nonlinearity)into a nonlinear Schrodinger equation (NLSE), has been derived from the Maxwell equationsin a nonlinear medium with the derivative-expansion procedure in the method of multi-scalesingular perturbation. Meanwhile its two equivalent expressions are given. First, the firstfourth-order perturbed equations of the Maxwell equations in a source-free nonlinear mediumwaveguide are obtained. Then, in the special case of the monomode waveguide, the third-or-der perturbed equation solution is the NLSE, and the fourth-order one is MNLSE. Carefulinvestigation shows that the MNLSE obtained with the reductive perturbation technique (Y.Kodama and A. Hasegawa, IEEE J. Quantum Electron, QE-23(1987), 510)should be corrected. 展开更多
关键词 nonlinear evolution equation optical soliton method of MULTI-SCALE SINGULAR perturbation.
原文传递
第一类导数非线性薛定谔方程的数值模拟 被引量:6
12
作者 李书存 曹俊杰 李文博 《北京信息科技大学学报(自然科学版)》 2016年第3期84-87,91,共5页
利用Taylor级数展开,给出了求解第一类导数非线性薛定谔方程的CrankNicolson格式。使用该格式对该方程进行数值模拟,数值算例验证了该格式具有保持时空2阶精度的性质。最后在初值上添加微小随机扰动,观察孤子解随时间的变化情况,结果显... 利用Taylor级数展开,给出了求解第一类导数非线性薛定谔方程的CrankNicolson格式。使用该格式对该方程进行数值模拟,数值算例验证了该格式具有保持时空2阶精度的性质。最后在初值上添加微小随机扰动,观察孤子解随时间的变化情况,结果显示孤子解在初值添加微小随机扰动后变化不大,说明孤子解具有很好的稳定性。 展开更多
关键词 导数非线性薛定谔方程 孤子解 CRANK-NICOLSON格式 随机扰动
下载PDF
一类KdV-Burgers方程的奇摄动解与孤子解 被引量:3
13
作者 包立平 李瑞翔 吴立群 《应用数学和力学》 CSCD 北大核心 2021年第9期948-957,共10页
讨论了一类具有大Reynolds数且弱频散性的KdV-Burgers方程,在数学上表示为一类奇摄动KdV-Burgers方程.KdV-Burgers方程中含有的非线性项与频散项互补作用形成稳定向前传播的孤立子.通过数学分析,描述了孤立子的传播途径和传播速度等物... 讨论了一类具有大Reynolds数且弱频散性的KdV-Burgers方程,在数学上表示为一类奇摄动KdV-Burgers方程.KdV-Burgers方程中含有的非线性项与频散项互补作用形成稳定向前传播的孤立子.通过数学分析,描述了孤立子的传播途径和传播速度等物理量的发展变化规律.通过奇摄动展开方法,构造了该问题的渐近解.首先,用Riemann-Earnshaw方法求得退化解,得到了简单波,该简单波波形中的任意一点与初始点都存在一个传播速度差,这使得波在传播过程中波形不断畸变,最终形成冲击波面,即间断面,在它的两侧质点的速度有一个跳跃,且随时间不断变化;其次,在退化解的间断曲面处做变量替换,构造一种修正的行波变换,得到了内解展开式的孤子解,并证明了内外解的存在性与唯一性;最后,通过一致有界逆算子的存在性做了余项估计,并得到渐近解的一致有效性.结果表明,KdV-Burgers方程在大Reynolds数且弱频散性的性质下,扰动集中在退化解的间断面附近,孤立子链接两侧质点,其传播途径不是时间与空间的线性形式,而是沿着退化解的间断面附近传播,形成稳定的波形. 展开更多
关键词 KDV-BURGERS方程 弱频散性 孤子解 奇摄动 一致有效性
下载PDF
双温非热尘埃等离子体中的二维尘埃声孤波 被引量:1
14
作者 张开彪 王红艳 +2 位作者 周志坚 向必纯 王永华 《信阳师范学院学报(自然科学版)》 CAS 2010年第2期204-207,共4页
使用约化摄动方法得到了高阶横向扰动下的含有双温非热离子的无磁化尘埃等离子体中的KP方程.研究结果表明,高阶横向扰动会使孤波的振幅减小,而使宽度增大,双温非热离子的存在会严重影响着尘埃声孤波的结构,而且,稀疏形孤波与压缩形孤波... 使用约化摄动方法得到了高阶横向扰动下的含有双温非热离子的无磁化尘埃等离子体中的KP方程.研究结果表明,高阶横向扰动会使孤波的振幅减小,而使宽度增大,双温非热离子的存在会严重影响着尘埃声孤波的结构,而且,稀疏形孤波与压缩形孤波均可能出现. 展开更多
关键词 尘埃声孤波 KP方程 双温非热离子 高阶横向扰动
下载PDF
微扰对Φ-4孤子的影响 被引量:1
15
作者 颜家壬 唐翌 《湖南师范大学自然科学学报》 CAS 1998年第2期17-22,共6页
发展了一种基于拉普拉斯变换的直接方法并用它研究了Φ-4方程的孤子微扰.应用这一方法求出了微扰对孤子的影响,即孤子参数对t1的依赖及一阶修正.
关键词 孤子 Φ-4方程 孤子微扰论 孤波
下载PDF
微扰Landau-Ginzburg-Higgs方程的保结构数值分析 被引量:1
16
作者 胡伟鹏 张宇 邓子辰 《西北工业大学学报》 EI CAS CSCD 北大核心 2012年第6期957-960,共4页
基于Hamilton变分原理,构造了微扰Landau-Ginzburg-Higgs方程的一阶广义多辛对称形式,随后对该形式采用多辛差分离散构造其保结构离散格式,最后通过计算机模拟,研究了微扰对Lan-dau-Ginzburg-Higgs方程孤子解的影响,为微扰动力学系统的... 基于Hamilton变分原理,构造了微扰Landau-Ginzburg-Higgs方程的一阶广义多辛对称形式,随后对该形式采用多辛差分离散构造其保结构离散格式,最后通过计算机模拟,研究了微扰对Lan-dau-Ginzburg-Higgs方程孤子解的影响,为微扰动力学系统的数值研究提供了新的途径。 展开更多
关键词 有限差分方法 哈密尔顿 孤子解 广义多辛 微扰Landau—Ginzburg-Higgs方程 保结构
下载PDF
光纤布拉格光栅中隙孤子的EPP方法分析 被引量:1
17
作者 李小路 江月松 《光学技术》 EI CAS CSCD 北大核心 2008年第2期269-271,共3页
提出了利用EPP方法分析光纤布拉格光栅中隙孤子的解。基于非线性耦合模式方程(NLCME)定性地分析了无微扰条件下的隙孤子参数与孤子的其它特性的关系。利用EPP方法分析了隙孤子的能量特性。证明了隙孤子的速度影响形态特性和能量分布。... 提出了利用EPP方法分析光纤布拉格光栅中隙孤子的解。基于非线性耦合模式方程(NLCME)定性地分析了无微扰条件下的隙孤子参数与孤子的其它特性的关系。利用EPP方法分析了隙孤子的能量特性。证明了隙孤子的速度影响形态特性和能量分布。从理论上解释了已观察到的一系列隙孤子的试验现象,对光纤布拉格光栅中产生隙孤子的应用具有理论意义。 展开更多
关键词 光纤布拉格光栅 隙孤子 非线性耦合模式方程 EPP方法 微扰
下载PDF
扰动非线性薛定谔方程的Painleve分析和精确孤立子解 被引量:2
18
作者 王烈衍 《宁波大学学报(理工版)》 CAS 1999年第2期37-41,共5页
指出扰动的非线性项仅在扰动项为零时,才具有Painleve性质.利用截断的Painleve分析方法得到了扰动非线性薛定谔方程的Backlund变换和5种形式的精确孤立子解.
关键词 薛定谔方程 P-分析 孤立子解 扰动 非线性
下载PDF
High-order numerical method for the derivative nonlinear Schrodinger equation 被引量:1
19
作者 Shu-Cun Li Xiang-Gui Li +1 位作者 Jun-Jie Cao Wen-Bo Li 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2017年第1期258-270,共13页
In this work,a fourth-order numerical scheme in space and two second-order numerical schemes in both time and space are proposed for the derivative nonlinear Schrodinger equation.We verify the mass conservation for th... In this work,a fourth-order numerical scheme in space and two second-order numerical schemes in both time and space are proposed for the derivative nonlinear Schrodinger equation.We verify the mass conservation for the two-level implicit scheme.The influence on the soliton solution by adding a small random perturbation to the initial condition is discussed.The numerical experiments are given to test the accuracy order for different schemes,respectively.We also test the conservative property of mass and Hamiltonian for these schemes from the numerical point of view. 展开更多
关键词 Derivative nonlinear Schrodinger equation finite difference soliton solution random perturbation
原文传递
含微扰Sine-Gordon方程的代数解法
20
作者 梅玉平 颜家壬 颜晓红 《湘潭大学自然科学学报》 CAS CSCD 1993年第4期63-65,共3页
本文采用一种新的方法研究单原子吸附的非线性动力学方程.将含微扰的Siue-Gordon方程转化为代数方程,进一步求得Sine-Gordon方程的解.该解的特点是当微扰为零时,结果与Sine-Gordon方程的标准解一致;微扰项的影响使解的对称性破缺,且破... 本文采用一种新的方法研究单原子吸附的非线性动力学方程.将含微扰的Siue-Gordon方程转化为代数方程,进一步求得Sine-Gordon方程的解.该解的特点是当微扰为零时,结果与Sine-Gordon方程的标准解一致;微扰项的影响使解的对称性破缺,且破缺程度的大小随着微扰的增加而增大。 展开更多
关键词 S-G方程 非线性动力学 代数解法
下载PDF
上一页 1 2 下一页 到第
使用帮助 返回顶部