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 共查询到19条相似文献,搜索用时 93 毫秒
1.
程雪苹  李金玉  薛江蓉 《物理学报》2011,60(11):110204-110204
利用Clarkson和Kruskal(CK)直接方法,对耦合KdV方程进行相似约化,同时从李群出发对该约化方程作了群论解释.进一步地,借助Ablowitz-Ramani-Segur(ARS)算法对耦合方程展开Painlevé测试,找到了3个Painlevé可积模型.最后通过形变映射法,求得耦合KdV方程的准确解析解. 关键词: 耦合KdV方程 CK直接法 Painlevé分析法 准确解析解  相似文献   

2.
具有阻尼项的非线性波动方程的相似约化   总被引:8,自引:0,他引:8       下载免费PDF全文
闫振亚  张鸿庆 《物理学报》2000,49(11):2113-2117
利用Clarkson和Kruskal引入的直接约化法,给出了具有阻尼项的非线性波动方程utt-2buxxt+αuxxxx=β(unx)x(α>0,β≠0,n≥2)三种类型的相似约化.从这些约化方程的Painlevé分析表明该方程在Ablowitz的猜测意义下是不可积的.此外还获得了该方程(n=2)的4种精确类孤波解. 关键词: 波动方程 相似约化 Painlevé分析 精确解  相似文献   

3.
李宁  刘希强 《物理学报》2013,62(16):160203-160203
利用修正的CK直接方法得到了Broer-Kau-Kupershmidt (简写为BKK)方程组的对称、约化, 通过解约化方程得到了该方程组的一些精确解, 包括双曲函数解、 三角函数解、 有理函数解、 艾里函数解、 幂级数解和 孤立子解等. 关键词: 修正的CK直接方法 BKK方程组 对称、约化 精确解  相似文献   

4.
郑连存  冯志丰  张欣欣 《物理学报》2007,56(3):1549-1554
从理论上研究了一类广义扩散方程的求解问题. 利用相似变换和解析拆分技巧给出了求解该类非线性微分方程近似解的一种有效方法, 方程的解可以表示为一个收敛的幂级数. 近似解结果和数值结果非常符合,证明了所提出的方法的准确性和可靠性, 该方法可以用于解决其他科学和工程技术问题. 关键词: 广义扩散方程 非线性边界值问题 解析拆分 近似解析解  相似文献   

5.
将直接微扰方法应用于含微扰的三维非线性Schrodinger方程,获得了该方程的包括零阶和一阶修正的近似解析解.借助得到的解析解,分析了微扰对孤子参数的影响.  相似文献   

6.
程雪苹  林机  韩平 《物理学报》2010,59(10):6752-6756
将直接微扰方法应用于含微扰的三维非线性Schrdinger方程,获得了该方程的包括零阶和一阶修正的近似解析解.借助得到的解析解,分析了微扰对孤子参数的影响。  相似文献   

7.
圆柱体相对转动动力学方程的积分解   总被引:7,自引:0,他引:7       下载免费PDF全文
董全林  王坤  张春熹  刘彬 《物理学报》2004,53(2):337-342
针对圆柱体任意两个横截面间的相对转动动力学方程,运用解耦方法获得方程的解析解,由于方程的特殊性,利用Jordan标准形求得可逆矩阵.从而得到了圆柱体相对转动动力学方程的积分形式的解.根据工程应用,给出了冲击性和周期性两类典型载荷作用下的解析解. 关键词: 相对转动 相似模拟 动力学方程 解析解  相似文献   

8.
张大军 《物理学报》2023,(10):26-37
本综述主要介绍了双线性约化方法在可积系统求解中的应用.这一方法基于双线性方法和解的双Wronskian表示.对于通过耦合系统约化而获得的可积方程,先求解未约化的耦合系统,给出用双Wronskian表示的解;进而利用双Wronskian的规则结构,施以适当的约化技巧,获得约化后的可积方程的解.以非线性Schr?dinger方程族和微分-差分非线性Schrodinger方程为具体例证,详述此方法的应用技巧.除了经典可积方程,该方法也适用于非局部可积系统的求解.其他例子还包括Fokas-Lenells方程和非零背景的非线性Schr?dinger方程等可积系统的求解.  相似文献   

9.
应用经典李群理论考虑了描述非平面冲击波形成和衰减现象的(1 1)维变系数Burgers方程,得到该方程的群分类及相应的对称.对于某些具体形式的色散项系数a(t)和非线性项系数b(t),给出了对应方程的对称约化及相似解.本文在已有基础上给出了方程新的显式解.这些解对于研究某些复杂的物理现象,以及验证数值求解法则的可行性有重要的意义.  相似文献   

10.
王振立  刘希强 《物理学报》2014,63(18):180205-180205
利用机械化算法得到了Kaup-Kupershmidt方程的非局域对称、约化,通过解约化方程得到了该方程的一些新的精确解.  相似文献   

11.
This paper studies the analytical and semi-analytic solutions of the generalized Calogero–Bogoyavlenskii–Schiff(CBS) equation. This model describes the(2 + 1)–dimensional interaction between Riemann-wave propagation along the y-axis and the x-axis wave. The extended simplest equation(ESE) method is applied to the model, and a variety of novel solitarywave solutions is given. These solitary-wave solutions prove the dynamic behavior of soliton waves in plasma. The accuracy of the obtained solution is verified using a variational iteration(VI) semi-analytical scheme. The analysis and the match between the constructed analytical solution and the semi-analytical solution are sketched using various diagrams to show the accuracy of the solution we obtained. The adopted scheme's performance shows the effectiveness of the method and its ability to be applied to various nonlinear evolution equations.  相似文献   

12.
An operator splitting method is proposed for the Degasperis–Procesi (DP) equation, by which the DP equation is decomposed into the Burgers equation and the Benjamin–Bona–Mahony (BBM) equation. Then, a second-order TVD scheme is applied for the Burgers equation, and a linearized implicit finite difference method is used for the BBM equation. Furthermore, the Strang splitting approach is used to construct the solution in one time step. The numerical solutions of the DP equation agree with exact solutions, e.g. the multipeakon solutions very well. The proposed method also captures the formation and propagation of shockpeakon solutions, and reveals wave breaking phenomena with good accuracy.  相似文献   

13.
A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well-known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values.  相似文献   

14.
王佳  李彪  叶望川 《中国物理 B》2010,19(3):30401-030401
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon-Schrdinger equation.The Homotopy analysis solutions of the Klein-Gordon-Schrdinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions.Through errors analysis and numerical simulation,we can see the approximate solution is very close to the exact solution.  相似文献   

15.
In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.  相似文献   

16.
In this Letter, variational iteration method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.  相似文献   

17.
In this article, a new version of the trial equation method is suggested. With this method, it is possible to find the new exact solutions of the nonlinear partial differential equations. The developed method is applied to unstable nonlinear Schrödinger equation. New exact solutions are expressed with Jacobi elliptic function solutions, 1-soliton solutions and rational function solutions. When the obtained results are examined, we can say the unstable nonlinear Schrödinger equation shows different dynamic behaviors. In addition, the physical behaviors of these new exact solution are given with two and three dimensional graphs.  相似文献   

18.
An analytical method for solving nonlinear equations with local forcing is proposed. It is shown in an example that a nonlinear forced equation may have many solutions, which generally do not turn to the solution of a linear equation in the limit of the nonlinear term becoming small. The solution of the Korteweg-de Vries (KdV) equation with forcing is applied to the problem of topographic Rossby vortices in shear flow. Solutions of other nonlinear equations with forcing are also obtained.  相似文献   

19.
Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.  相似文献   

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