共查询到18条相似文献,搜索用时 93 毫秒
1.
General Jacobian elliptic function expansion method and its applications 总被引:11,自引:0,他引:11 下载免费PDF全文
An extended Jacobian elliptic function expansion method is presented and successfully applied to the nonlinear SchrSdinger (NLS) equation and Zakharov equation. We obtain some new solutions besides Fu et al‘s results. The results show that our method is more powerful to construct Jacobian elliptic function and can be applied to other nonlinear physics systems. 相似文献
2.
ZHENG Ying ZHANG Yuan-Yuan ZHANG Hong-Qing 《理论物理通讯》2006,46(1):5-9
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2+1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations. 相似文献
3.
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems. 相似文献
4.
New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional KP equation with variable coefficients 下载免费PDF全文
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients. 相似文献
5.
FUZun-Tao LIUShi-Da LIUShi-Kuo 《理论物理通讯》2003,40(3):285-292
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems. 相似文献
6.
CHEN Jiang HE Hong-Sheng YANG Kong-Qing 《理论物理通讯》2005,44(2):307-310
A generalized F-expansion method is introduced and applied to (3+1 )-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics. 相似文献
7.
Solutions to Generalized mKdV Equation 总被引:13,自引:0,他引:13
FUZun-Tao DENGLian-Tang LIUShi-Kuo LIUShi-Da 《理论物理通讯》2003,40(6):641-644
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
8.
YANG Xian-Lin TANG Jia-Shi 《理论物理通讯》2008,50(11):1047-1051
The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including solitary wave solutions, trigonometric function solutions and Jacobi elliptic doubly periodic function solutions, some of which are new exact solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
9.
An Automated Jacobi Elliptic Function Method for Finding Periodic Wave Solutions to Nonlinear Evolution Equation 下载免费PDF全文
We describe the Jacobi elliptic function method for finding exact periodic wave solutions to nonlinear evolution equations.We present a Maple packaged automated Jacobi elliptic function method,which can entirely automatically output the exact periodic wave solutions.The effectiveness of the automated Jacobi elliptic function method is demonstrated using as examples the spplication to a variety of equations with physical interest.Not only are the previously known solutions recovered but in some cases new solutions and more general forms of solutions are obtained. 相似文献
10.
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions. 相似文献
11.
YAN Zhen-Ya 《理论物理通讯》2002,38(10)
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations. 相似文献
12.
YAN Zhen-Ya 《理论物理通讯》2003,39(2)
More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations. 相似文献
13.
In this Letter, the Fan sub-equation method is used to construct exact solutions of a generalized Hirota-Satsuma coupled KdV equation. Many exact traveling wave solutions are successfully obtained, which contain more general solitary wave solutions and Jacobian elliptic function solutions with double periods. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations. 相似文献
14.
15.
LIU Cheng-Shi 《理论物理通讯》2005,44(5):799-801
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations. 相似文献
16.
提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式,再利用三阶多项式的完 全判别系统求解,由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解
关键词:
试探方程法
非线性发展方程
孤波解
Jacobi椭圆函数
周期解 相似文献
17.
Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation 下载免费PDF全文
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 相似文献