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1.
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
2.
CHEN Jiang YANG Kong-Qing HE Hong-Sheng 《理论物理通讯》2007,48(5):877-880
A new generalized F-expansion method is introduced and applied to the study of the (2+1)-dimensional Boussinesq equation. The further extension of the method is discussed at the end of this paper. 相似文献
3.
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained. 相似文献
4.
The Periodic Wave Solutions for Two Nonlinear Evolution Equations 总被引:14,自引:0,他引:14
ZHANGJin-Liang WANGMing-Liang CHENGDong-Ming FANGZong-De 《理论物理通讯》2003,40(2):129-132
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobi elliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained. 相似文献
5.
HUANG Wen-Hua 《理论物理通讯》2006,46(10)
A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. As an application of this method, we study the (2 1)-dimensional dispersive long wave equation. With the aid of computerized symbolic computation, a number of doubly periodic wave solutions expressed by various Jacobi elliptic functions are obtained. In the limit cases, the solitary wave solutions are derived as well. 相似文献
6.
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
7.
DOU Fu-Quan SUN Jian-An DUAN Wen-Shan SHI Yu-Ren LÜ Ke-Pu HONG Xue-Ren 《理论物理通讯》2006,45(6):1063-1068
With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for
constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing
methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional
Kadomtsev-Petviashvili equation to illustrate our method. As a
result, twenty families of periodic solutions are obtained. Of
course, more solitary wave solutions, shock wave solutions or
triangular function formal solutions can be obtained at their limit
condition. 相似文献
8.
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 Jacobi elliptic function of nonlinear partial differential equations (NPDEs). 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
9.
Elliptic equation is taken as an ansatz and applied to solve
nonlinear wave equations directly. More kinds of solutions are
directly obtained, such as rational solutions, solitary wave
solutions, periodic wave solutions and so on. It is shown that
this method is more powerful in giving more kinds of solutions, so
it can be taken as a generalized method. 相似文献
10.
Solving Nonlinear Wave Equations by Elliptic Equation 总被引:5,自引:0,他引:5
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. 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 it can be taken as a generalized method. 相似文献
11.
A New Approach to Solve Nonlinear Wave Equations 总被引:3,自引:0,他引:3
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions. 相似文献
12.
An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained. 相似文献
13.
FU Zun-Tao LIU Shi-Kuo LIU Shi-Da 《理论物理通讯》2004,42(9)
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on. 相似文献
14.
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, 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
15.
Elliptic Equation and New Solutions to Nonlinear Wave Equations 总被引:2,自引:0,他引:2
FUZun-Tao LIUShi-Kuo LIUShi-Da 《理论物理通讯》2004,42(3):343-346
The new solutions to elliptic equation are shown, and then the elliptic: equation is taken as a transformation and is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on. 相似文献
16.
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
17.
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 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively. 相似文献
18.
YAN Zhen-Ya 《理论物理通讯》2002,38(2):143-146
An extended Jacobian elliptic function
expansion method presented recently by us is applied to the mKdV equation such
that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus
m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to
other nonlinear differential
equations. 相似文献
19.
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
20.
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