共查询到20条相似文献,搜索用时 93 毫秒
1.
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
2.
BAI Cheng-Jie HAN Ji-Guang WANG Wei-Tao AN Hong-Yong 《理论物理通讯》2008,49(5):1241-1244
The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort. 相似文献
3.
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
4.
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
5.
YANZhen-Ya 《理论物理通讯》2004,42(5):645-648
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献
6.
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
7.
ZHANG Ling ZHANG Li-Feng LI Chong-Yin WANG Tie TAN Yan-Ke 《理论物理通讯》2008,49(6):1557-1560
By using the modified mapping method, we find new exact solutions of the Petviashvili 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
8.
In this letter, the modified Jacobi elliptic function expansion method is extended to solve M-coupled KdV equation, M-coupled Ito equation, vKdV equation, and AKNS equation. Some new Jacobi elliptic function solutions are obtained by using Mathematica. When the modulus m → 1, those periodic solutions degenerate as the corresponding soliton solutions. 相似文献
9.
WANG Yue-Ming LI Xiang-Zheng YANG Sen WANG Ming-Liang 《理论物理通讯》2005,44(3):396-400
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively. 相似文献
10.
SHEN Shou-Feng ZHANG Jun YE Cai-Er PAN Zu-Liang 《理论物理通讯》2005,44(4):604-608
In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger (NLS) system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions. 相似文献
11.
BAI Cheng-Lin BAI Cheng-Jie ZHAO Hong 《理论物理通讯》2005,44(5):821-826
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions. 相似文献
12.
LIU Shi-Kuo FU Zun-Tao WANG Zhang-Gui LIU Shi-Da 《理论物理通讯》2008,49(5):1155-1158
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained. 相似文献
13.
Extended Jacobi elliptic function method and its applications to (2+l)-dimensional dispersive long-wave equation 下载免费PDF全文
An extended Jacobi elliptic function method is proposed for constructing the exact double periodic solutions of nonlinear partial differential equations (PDEs) in a unified way. It is shown that these solutions exactly degenerate to the many types of soliton solutions in a limited condition. The Wu-Zhang equation (which describes the (2+1)-dimensional dispersive long wave) is investigated by this means and more formal double periodic solutions are obtained. 相似文献
14.
SONG Li-Na ZHANG Hong-Qing 《理论物理通讯》2007,47(6):969-974
In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+ 1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions. 相似文献
15.
LI De-Sheng LUO Cheng-Xin 《理论物理通讯》2006,46(2):193-198
In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2+1)-dimensional spaces. Some new elliptic function" solutions are obtained. 相似文献
16.
Periodic Wave Solutions to Dispersive Long-Wave Equations in (2+1)-Dimensional Space 总被引:2,自引:0,他引:2
TIANYing-Hui CHENHan-Lin LIUXi-Qiang 《理论物理通讯》2005,44(1):8-10
Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solitary wave solutions are obtained as well. 相似文献
17.
In this paper, by means of double elliptic equation expansion approach, the novel double nonlinear wave solutions of the (2+1)-dimensional break soliton equation are obtained. These double nonlinear wave solutions contain the double Jacobi elliptic function-like solutions, the double solitary wave-like solutions, and so on. The method is also powerful to some other nonlinear wave equations in (2+1) dimensions. 相似文献
18.
Exact analytical solutions of three-dimensional Gross-Pitaevskii equation with time-space modulation 下载免费PDF全文
By the generalized sub-equation expansion method and symbolic computation,this paper investigates the(3 + 1)dimensional Gross-Pitaevskii equation with time-and space-dependent potential,time-dependent nonlinearity,and gain or loss.As a result,rich exact analytical solutions are obtained,which include bright and dark solitons,Jacobi elliptic function solutions and Weierstrass elliptic function solutions.With computer simulation,the main evolution features of some of these solutions are shown by some figures.Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management. 相似文献
19.
An Automated Algebraic Method for Finding a Series of Exact Travelling Wave Solutions of Nonlinear Evolution Equations 总被引:2,自引:0,他引:2 下载免费PDF全文
Based on a type of elliptic equation,a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed,meanwhile,its complete implementation TRWS in Maple is presented.The TRWS can output a series of travelling wave solutions entirely automatically,which include polynomial solutions,exponential function solutions,triangular function solutions,hyperbolic function solutions,rational function solutions,Jacobi elliptic function solutions,and Weierstrass elliptic function solutions.The effectiveness of the package is illustrated by applying it to a variety of equations.Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained. 相似文献
20.
ZHAO Xue-Qin ZHI Hong-Yan 《理论物理通讯》2008,50(8):309-314
With the aid of computerized symbolic computation, an improved F-expansion method is presented to uniformly construct more new exact doubly periodic solutions in terms of rational formal Jscobi elliptic function of nonlinear partial differential equations (NPDFs). The coupled Drinfel'd-Sokolov-Wilson equation is chosen to illustrate the method. As a result, we can successfully obtain abundant new doubly periodic solutions without calculating various Jacobi elliptic functions. In the limit cases, the rational solitary wave solutions and trigonometric function solutions are obtained as well. 相似文献