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1.
New Periodic Solution to Jacobi Elliptic Functions of a (2+1)-Dimensional BKP Equation and a Generalized Klein-Gordon Equation
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With the help of the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to obtain the Jacobi doubly periodic wave solutions of the (2+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and the generalized Klein-Gordon equation. The method is also valid for other (1+1)-dimensional and higher dimensional 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.
YAN Zhen-Ya 《理论物理通讯》2005,43(3):391-396
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem
solving soliton equations into
another one solving the corresponding set of nonlinear algebraic equations.
With the aid of Maple, we choose the modified KdV equation,
(2+1)-dimensional KP equation,
and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm.
As a consequence, many types of new doubly periodic solutions are obtained
in terms of the Weierstrass elliptic function. Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple
limits of doubly periodic solutions. 相似文献
4.
New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 总被引:1,自引:0,他引:1
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In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 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.
A series of new double periodic solutions to a (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation
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By means of a new general ans?tz and with the aid of symbolic computation, a new algebraic method named Jacobi elliptic function rational expansion is devised to uniformly construct a series of new double periodic solutions to (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation in terms of rational Jacobi elliptic function. 相似文献
7.
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
8.
PENG Yan-Ze 《理论物理通讯》2005,43(2):205-207
New exact solutions in terms of the Jacobi
elliptic functions are obtained to the (2+1)-dimensional breaking
soliton equation by means of the modified mapping method. Limit
cases are studied, and new solitary wave solutions and triangular
periodic wave solutions are obtained. 相似文献
9.
With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition. 相似文献
10.
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
11.
New exact solutions of the (2 +1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions. 相似文献
12.
By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrǒdinger equation 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
13.
New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional KP equation with variable coefficients
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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
14.
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
15.
LIU Guan-Ting 《理论物理通讯》2008,49(2):287-290
Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Backlund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass & function. Some of them are novel. 相似文献
16.
Extended Jacobi elliptic function method and its applications to (2+l)-dimensional dispersive long-wave equation
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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
17.
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
18.
19.
New Doubly Periodic Solutions of Nonlinear Evolution Equations via Weierstrass Elliptic Function Expansion Algorithm 总被引:1,自引:0,他引:1
YAN Zhen-Ya 《理论物理通讯》2004,42(11)
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 correspondingsystem 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
20.
The sinh-Gordon equation expansion method is further extended by generalizing 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