共查询到18条相似文献,搜索用时 109 毫秒
1.
The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions (including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions) for the new (2+1)-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field. 相似文献
2.
YANG Zong-Hang 《理论物理通讯》2006,46(5):807-811
An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guldeline to classifj, the various types of the solution according to some parameters. 相似文献
3.
HUANG Wen-Hua LIU Yu-Lu ZHANG Jie-Fang LAI Xian-Jing 《理论物理通讯》2005,44(3):401-406
We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations of the periodic solutions to the (2+1)-dimensional KdV equations obtained by means of the Jacobian elliptic function method, but they possess different periods and velocities. 相似文献
4.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(5):807-809
The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献
5.
In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+ 1)-dimensional KK equation by the symmetry method and the (G1/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. 相似文献
6.
PENGYan-Ze 《理论物理通讯》2003,40(3):257-258
A new Baecklund transformation for (2 1)-dimensional KdV equation is first obtained by using homogeneous balance method. And making use of the Baecklund transformation and choosing a special seed solution, we get special types of solitary wave solutions. Finally a general variable separation solution containing two arbitrary functions is constructed, from which abundant localized coherent structures of the equation in question can be induced. 相似文献
7.
CHEN Yong YAN Zhen-Ya 《理论物理通讯》2005,44(5):789-792
Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of (2+1)- dimensional generalization of mKdV equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this (2+1)-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions. 相似文献
8.
In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given. 相似文献
9.
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
10.
CHENYong WANGQi LIBiao 《理论物理通讯》2004,42(5):655-660
We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2 1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions‘soliton-like solutions, double-like periodic and trigonometric-like function solutions. 相似文献
11.
BIAN Xue-Jun 《理论物理通讯》2005,44(11)
An algebraic method is proposed to solve a new (2 1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions. 相似文献
12.
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
13.
Conditional Similarity Solutions of (2+1)—Dimensional General nonintegrable KdV Equation 总被引:1,自引:0,他引:1
TANGXiao-Yan LOUSen-Yue 《理论物理通讯》2002,37(2):139-144
The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model.To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters.In this paper,we make a modification for the usual direct method to find some conditional similarity solutions of a (2 1)-dimensional general nonintegrable KdV equation. 相似文献
14.
PENG Yan-ze 《理论物理通讯》2003,40(9)
A new Backlund transformation for (2 1)-dimensional KdV equation is first obtained by using homogeneousbalance method. And making use of the Backlund transformation and choosing a special seed solution, we get specialtypes of solitary wave solutions. Finally a general variable separation solution containing two arbitrary functions isconstructed, from which abundant localized coherent structures of the equation in question can be induced. 相似文献
15.
In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G, /G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. 相似文献
16.
A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System 总被引:1,自引:0,他引:1
BAI Cheng-Jie ZHAO Hong 《理论物理通讯》2007,48(5):801-810
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on (2+1)-dimensional dispersive long-wave equation. 相似文献
17.
PENG Yan-Ze 《理论物理通讯》2004,41(5):669-670
A new multisoliton solution to the
(2+1)-dimensional KdV equation is obtained by means of the
truncated Painleve expansion method and a direct ansatz technique.
This new exact solution is periodic in the propagating direction
x and exponentially decaying in y and thus it is called
periodic solitons. A typical spatial structure of it is
illustrated by the figures. 相似文献
18.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(11)
The singular manifold method is used to obtain two general solutions to a (2 1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献