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1.
《Waves in Random and Complex Media》2013,23(1):30-41
An extended Fan sub-equation method is used to seek some new and more general traveling wave solutions of nonlinear Schrödinger equation (NLSE). The important fact of this method is to take the full advantage of clear relationship among general elliptic equation involving five parameters and other existing sub-equations involving three parameters. It is preferable to use this method to solve NLSE because this method gives us all the solutions obtained previously by the application of at least four methods (the method of using Riccati equation, or auxiliary ordinary differential equation method, or first kind elliptic equation or the generalized Riccati equation as mapping equation) in a unified manner. So it is shown that this method is concise and its applications are promising. 相似文献
2.
Yusuf Z. Umul 《Optics & Laser Technology》2010,42(8):1323-1327
The paraxial wave equation is a reduced form of the Helmholtz equation. Its solutions can be directly obtained from the solutions of the Helmholtz equation by using the method of complex point source. We applied the same logic to quantum mechanics, because the Schrödinger equation is parabolic in nature as the paraxial wave equation. We defined a differential equation, which is analogous to the Helmholtz equation for quantum mechanics and derived the solutions of the Schrödinger equation by taking into account the solutions of this equation with the method of complex point source. The method is applied to the problem of diffraction of matter waves by a shutter. 相似文献
3.
《Waves in Random and Complex Media》2013,23(4):559-590
This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis. 相似文献
4.
New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation 总被引:2,自引:0,他引:2
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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. 相似文献
5.
6.
LIU Cheng-Shi 《理论物理通讯》2006,45(2):219-223
A trial equation method to nonlinear evolution equation
with rank inhomogeneous is given. As applications, the exact
traveling wave solutions to some higher-order nonlinear equations
such as generalized Boussinesq equation, generalized Pochhammer-Chree
equation, KdV-Burgers equation, and KS equation and so on, are
obtained. Among these, some results are new. The proposed method is
based on the idea of reduction of the order of ODE. Some mathematical
details of the proposed method are discussed. 相似文献
7.
8.
对(G′/G)展开法做了进一步的研究,利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题.借助Riccati方程的B?cklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解.这样,利用(G′/G)展开法可以获得非线性发展方程的无穷序列解,这一方法是对已有方法的扩展,与已有方法相比可获得更丰富的无穷序列解.以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解.这一方法可以用来构造其他非线性发展方程的无穷序列解. 相似文献
9.
New Periodic Solution to Jacobi Elliptic Functions of a (2+1)-Dimensional BKP Equation and a Generalized Klein-Gordon Equation
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With the help of the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to obtain the Jacobi doubly periodic wave solutions of the (2+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and the generalized Klein-Gordon equation. The method is also valid for other (1+1)-dimensional and higher dimensional systems. 相似文献
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11.
In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation. 相似文献
12.
一维多介质可压缩Euler方程的高精度RKDG有限元方法 总被引:3,自引:0,他引:3
采用RKDG有限元目的、Level Set目的和改进的带"Isentropic"修正的Ghost Fluid目的模拟了一维多介质可压缩Euler方程,其中Euler方程、Level Set方程和重新初始化方程都采用了三阶精度的RKDG有限元目的进行离散,并对一维两种介质可压缩流体进行了数值实验,得到了较高分辨率的计算结果. 相似文献
13.
In this paper, we present the local discontinuous Galerkin method for solving Burgers’ equation and the modified Burgers’ equation. We describe the algorithm formulation and practical implementation of the local discontinuous Galerkin method in detail. The method is applied to the solution of the one-dimensional viscous Burgers’ equation and two forms of the modified Burgers’ equation. The numerical results indicate that the method is very accurate and efficient. 相似文献
14.
LIU Cheng-Shi 《理论物理通讯》2006,45(3):395-397
As an improved version of trial equation method,
a new trial equation method is proposed. Using this method,
abundant new exact traveling
wave solutions to a high-order KdV-type equation are obtained. 相似文献
15.
The Schrödinger–KdV equation with power-law nonlinearity is studied in this paper. The solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The G′/G method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy perturbation method are also applied to solve this equation. The numerical simulations are also given. 相似文献
16.
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. 相似文献
17.
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
18.
将冯康和余德浩提出的自然边界归化方法[1~4]应用于求解抛物方程初边值外区域问题,提出一种自然边界元与有限元耦合算法。先将控制方程对时间进行离散化,得到关于时间步长的离散化格式,给出圆外域上的自然积分方程,基于此研究抛物方程无界区域问题的自然边界元与有限元耦合法,最后给出相应的数值例子。 相似文献
19.
LIU Chun-Ping 《理论物理通讯》2011,56(2):223-227
A modified homogeneous balance method is proposed by improving some key steps in the homogeneous balance method. Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneous balance method. Generalized Boussinesq equation, KP equation, and mKdV equation are chosen as examples to llustrate our method. This approach is also applicable to a large variety of nonlinear evolution equations. 相似文献
20.
本文推导了考虑中子之间碰撞的非线性中子输运方程,提出了求解该方程的n-n逐次碰撞展开法,并利用此方法把方程化为适于数值求解的线性输运方程组的形式,编制计算程序进行了数值计算,讨论了解的物理意义。 相似文献