共查询到20条相似文献,搜索用时 31 毫秒
1.
M. A. Abdou 《Nonlinear dynamics》2008,52(1-2):95-102
In this paper, a generalized auxiliary equation method with the aid of the computer symbolic computation system Maple is proposed to construct more exact solutions of nonlinear evolution equations, namely, the higher-order nonlinear Schrödinger equation, the Whitham–Broer–Kaup system, and the generalized Zakharov equations. As a result, some new types of exact travelling wave solutions are obtained, including soliton-like solutions, trigonometric function solutions, exponential solutions, and rational solutions. The method is straightforward and concise, and its applications are promising. 相似文献
2.
By means of the auxiliary ordinary differential equation method, we have obtained many solitary wave solutions, periodic wave solutions and variable separation solutions for the (2+1)-dimensional KP equation. Using a mixed method, many exact solutions have been obtained. 相似文献
3.
李继彬 《应用数学和力学(英文版)》2008,29(11):1391-1398
By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained. 相似文献
4.
李继彬 《应用数学和力学(英文版)》2008,29(4):437-440
By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given. 相似文献
5.
This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the
Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical
system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given. 相似文献
6.
This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form. 相似文献
7.
The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type.In different regions of the parametric space,sufficient conditions to guarantee the existence of solitary wave solutions,periodic wave solutions,kink and anti-kink wave solutions are given.All possible exact explicit parametric representations are obtained for these waves. 相似文献
8.
The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper,
the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then
solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no
exact solution. Travelling wave solutions are also obtained. 相似文献
9.
Exact solutions to the Korteweg-de Vries-Burgers equation 总被引:2,自引:0,他引:2
We introduce a transormation which reduces the Korteweg-de Vries-Burgers (KdVB) equation, ut + 2auux + 5buxx + cuxxx = 0, to a quadratic form involving a new dependent variable and its partial derivatives. Exact solutions of the KdVB equation can be obtained by solving this equation. The exact form of the travelling wave solution to the KdVB equation is obtained in this paper, and its nature depends on the direction of propagation of the wave. 相似文献
10.
In the present paper, we study a non-linear reaction-diffusion equation, which can be considered as a generalized Fisher equation. An exact solution and traveling wave solutions to the generalized Fisher equation are obtained by means of the Cole-Hopf transformation and the Lie symmetry method. 相似文献
11.
12.
用离散速度方法计算浅水长波方程 总被引:1,自引:0,他引:1
用离散速度法计算浅水波方程,将空气动力学方程和浅水波方程作了比较,用Nadiga提出的近平衡流动方法模拟浅水波方程的连续和间断解。计算了一维的溃坝波问题和Thacker提出的连续解问题,结果与精确解作了比较,并且计算了水流跃过障碍物的问题。 相似文献
13.
Jibin Li 《Journal of Dynamics and Differential Equations》2008,20(4):909-922
Using the method of dynamical systems for six nonlinear wave equations, the exact explicit parametric representations of the
solitary cusp wave solutions and the periodic cusp wave solutions are given. These parametric representations follow that
when travelling systems corresponding to these nonlinear wave equations has a singular straight line, under some parameter
conditions, nonanalytic travelling wave solutions must appear.
Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday 相似文献
14.
We provide travelling wave solutions of the equation for foam drainage in porous media, taking into account an additional
symmetry requirement. The method of solution used is reminescent of the approach developed to treat the Rapoport–Leas equation
for two-phase flow. Numerical solutions are also presented and compared to the analytical ones. 相似文献
15.
吕咸青 《应用数学和力学(英文版)》1993,14(11):1013-1018
By using the methods of mathematics analysis,we investigate the travelling wave solution of the KdVB equation under the assumption v~2》4μ.We prove that the travelling wave solution is quantitatively similar to the corresponding Burgers shock wave.Then we prove that the absolute error of the general asymptotic expansion is high order quantity of the small parameterε. 相似文献
16.
When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM),singularities in the local boundary integrals need to be treated specially. In the current paper,local integral equations are adopted for the nodes inside the domain trod moving least square approximation (MLSA) for the nodes on the global boundary,thus singularities will not occur in the new al- gorithm.At the same time,approximation errors of boundary integrals are reduced significantly.As applications and numerical tests,Laplace equation and Helmholtz equa- tion problems are considered and excellent numerical results are obtained.Furthermore, when solving the Hehnholtz problems,the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions.Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number. 相似文献
17.
《Wave Motion》2020
We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili method for solving the Rosenau equation with single or double power law nonlinearity. Numerical calculations rely on a uniform discretization of a finite computational domain. Through some numerical experiments we observe that the algorithm converges rapidly and it is robust to very general forms of the initial guess. 相似文献
18.
Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given. 相似文献
19.
In this paper, using the Lie symmetry analysis method, we study the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. The similarity reductions and exact solutions for the equation are obtained. Then the exact analytic solutions are considered by the power series method, and the physical significance of the solutions is considered from the transformation group point of view. 相似文献
20.
In this paper, with the aid of computer symbolic computation system such as Maple, an algebraic method is firstly applied
to two nonlinear evolution equations, namely, nonlinear Schrodinger equation and Pochhammer–Chree (PC) equation. As a consequence,
some new types of exact traveling wave solutions are obtained, which include bell and kink profile solitary wave solutions,
triangular periodic wave solutions, and singular solutions. The method is straightforward and concise, and it can also be
applied to other nonlinear evolution equations in mathematical physics. 相似文献