共查询到19条相似文献,搜索用时 93 毫秒
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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
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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
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Mostafa M A Khater S K Elagan M A El-Shorbagy S H Alfalqi J F Alzaidi Nawal A Alshehri 《理论物理通讯》2021,73(9):95003
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
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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
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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
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Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method 下载免费PDF全文
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon-Schrdinger equation.The Homotopy analysis solutions of the Klein-Gordon-Schrdinger 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
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Mehmet Senol 《理论物理通讯》2020,72(5):55003-31
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
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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
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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
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E. A. Novikov 《Physica D: Nonlinear Phenomena》1986,20(2-3):423-428
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
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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