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1.
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.
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.
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
4.
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
5.
LI De-Sheng LUO Cheng-Xin 《理论物理通讯》2006,46(8)
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
6.
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations.
With the aid of symbolic computation, we apply the proposed method
to solving the (1+1)-dimensional dispersive long wave equation and
explicitly construct a series of exact solutions which include the
rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases. 相似文献
7.
Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations 总被引:1,自引:0,他引:1
The Jacobi elliptic function expansion method is extended to derive the
explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are
chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi
elliptic cosine function and the third elliptic function solutions
are obtained. It is shown that the shock wave solutions and
solitary wave solutions can be obtained at their limit condition. 相似文献
8.
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
9.
WEN Xiao-Yong 《理论物理通讯》2008,49(5):1235-1240
With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation are constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m →0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions. 相似文献
10.
ZHAOQiang LIUShi-Kuo FUZun-Tao 《理论物理通讯》2004,42(2):239-241
The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained. 相似文献
11.
DOU Fu-Quan SUN Jian-An DUAN Wen-Shan LU Ke-Pu 《理论物理通讯》2007,48(4):584-590
Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the (3+1)-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures (new dromions) are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures (dromions) are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic. 相似文献
12.
GONG Lun-Xun PAN Jun-Ting 《理论物理通讯》2007,48(5):787-790
The modified mapping method is further improved by the expanded expression of u(ξ) that contains the terms of the first-order derivative of function f(ξ). Some new exact solutions to the mBBM equation are determined by means of the method. We can obtain many new solutions in terms of the Jacobi elliptic functions of the equation. 相似文献
13.
YAN Zhen-Ya 《理论物理通讯》2002,38(8)
An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu‘s allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations. 相似文献
14.
Utilizing the Wronskian technique, a combined Wronskian condition is established for a (3+1)-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed. 相似文献
15.
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
16.
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
17.
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
18.
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
19.
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
20.
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