共查询到20条相似文献,搜索用时 10 毫秒
1.
Explicit exact solitary wave solutions for generalized symmetric regualrized long—wave equations with high—order nonlinear terms 总被引:2,自引:0,他引:2
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper,we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by meas of proper transformation and undeterined assumption method. 相似文献
2.
Using symbolic computation to construct travelling wave solutions to nonlinear partial differential equations
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Based upon the symbolic computation and the coupled projective Riccati equation, the tanh function method is further improved. As its applications, Wu-Zhang equation (which describes a (2+1)-dimensional dispersive long wave) and the (1+1)-dimensional dispersive long wave equation obtained from Wu-Zhang equation by scaling transformation and symmetry reduction are chosen to illustrate the validity of the proposed approach. 相似文献
3.
Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions. 相似文献
4.
New multi—soliton solutions and travelling wave solutions of the dispersive long—wave equations 总被引:7,自引:0,他引:7
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Using the extended homogeneous balance method,the (1 1)-dimensional dispersive long-wave equations have been solved.Starting from the homogeneous balance method,we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation.Usually,we can obtain only a type of soliton-like solution.In this paper,we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation. 相似文献
5.
6.
7.
Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. 相似文献
8.
Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
下载免费PDF全文
![点击此处可从《物理学报》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. 相似文献
9.
This paper presents a meshless method for the nonlinear generalized regularized long wave(GRLW) equation based on the moving least-squares approximation.The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method.A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm.Compared with numerical methods based on mesh,the meshless method for the GRLW equation only requires the scattered nodes instead of meshing the domain of the problem.Some examples,such as the propagation of single soliton and the interaction of two solitary waves,are given to show the effectiveness of the meshless method. 相似文献
10.
Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, the travelling wave solutions for the generalized
Burgers--Huxley equation with nonlinear terms of any order are
studied. By using the first integral method, which is based on the
divisor theorem, some exact explicit travelling solitary wave
solutions for the above equation are obtained. As a result, some
minor errors and some known results in the previousl literature
are clarified and improved. 相似文献
11.
采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
关键词:
齐次平衡法
孤子解
孤波解
广义Boussinesq方程
bidirectional Kaup-Kupershmi dt方程 相似文献
12.
In this paper, the generally projective Riccati equations method is improved by means of a generalized transformation. The improved method can be applied to find not only some exact travelling wave solutions but also some soliton-like solutions with the aid of symbolic computation system — Maple. We choose Wick-type stochastic mKdV equations to illustrate the method. As a result, some stochastic soliton-like solutions are obtained. 相似文献
13.
Huiqun Zhang 《Reports on Mathematical Physics》2007,60(1):97-106
A direct algebraic method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases. The scheme is implemented for obtaining multiple soliton solutions of the generalized Zakharov equations, and then new exact travelling wave solutions with complex phases are obtained. In addition, by using new exact solutions of an auxiliary ordinary differential equation, new exact travelling wave solutions for the generalized Zakharov equations are obtained. 相似文献
14.
New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov Equations Using General Projective Riccati Equation Method 总被引:1,自引:0,他引:1
Applying the generalized method, which is a
direct and unified algebraic method for constructing multiple
travelling wave solutions of nonlinear partial differential
equations (PDEs), and implementing in a computer
algebraic system, we consider the generalized Zakharov-Kuzentsov equation
with nonlinear terms of any order. As a result, we can not only
successfully recover the previously known travelling wave solutions
found by existing various tanh methods and other sophisticated methods,
but also obtain some new formal solutions. The solutions obtained include
kink-shaped solitons, bell-shaped solitons,
singular solitons, and periodic solutions. 相似文献
15.
By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions. 相似文献
16.
The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Using the projective Riccati equation expansion (PREE) method, new
families of variable separation solutions (including solitary wave
solutions, periodic wave solutions and rational function solutions)
with arbitrary functions for two nonlinear physical models are
obtained. Based on one of the variable separation solutions and by
choosing appropriate functions, new types of interactions between
the multi-valued and single-valued solitons, such as a peakon-like
semi-foldon and a peakon, a compacton-like semi-foldon and a
compacton, are investigated. 相似文献
17.
18.
The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed. 相似文献
19.
20.
Symbolic Computation and Construction of Soliton-Like Solutions to the(2+1)-Dimensional Breaking Soliton Equation 总被引:2,自引:0,他引:2
Based on the computerized symbolic system Maple, a new generalized expansion method of Riccatiequation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new generalansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = 0, uy = vx, and obtain rich new families of the exact solutions of the breaking soliton equation, including thenon-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular functionsolutions. 相似文献