共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
The weak Darboux transformation of the (2+1) dimensional Euler equation is used to find its exact solutions. Starting from a constant velocity field solution, a set of quite general periodic wave solutions such as the Rossby waves can be simply obtained from the weak Darboux transformation with zero spectral parameters. The constant vorticity seed solution is utilized to generate Bessel waves. 相似文献
3.
CAO Ce-Wen YANG Xiao 《理论物理通讯》2008,49(1):31-36
Special solution of the (2+1)-dimensional Sawada Kotera equation is decomposed into three (0+1)- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy. 相似文献
4.
Using the modified CK's direct method, we derive a symmetry group theorem of (2+1)-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of (2+1)- dimensional dispersive long-wave equations are obtained. 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.
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
7.
Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev-Petviashvili Equation 总被引:2,自引:0,他引:2 下载免费PDF全文
Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtadned. 相似文献
8.
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
9.
An integrable (2+1)-dimensional coupled mKdV equation is decomposed into two (1 +1)-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two (1+1)-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained. 相似文献
10.
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schr6dinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1 + 1 )-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method. 相似文献
11.
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
12.
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
13.
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2007,48(3):405-410
In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation. 相似文献
14.
DONG Zhong-Zhou LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(1):15-20
Using the classical Lie method of infinitesimals, we first obtain the symmetry of the (2+1)-dimensional Burgers-Korteweg-de-Vries (3D-BKdV) equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation. 相似文献
15.
In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groups, of the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified direct method proposed by Lou [J.Phys.A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained and the relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groups obtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equations are constructed by the relationship obtained in the paper between the new solution and known solution. 相似文献
16.
MA Song-Hua FANG Jian-Ping HONG Bi-Hai ZHENG Chun-Long 《理论物理通讯》2008,49(5):1245-1248
By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is derived. Based on the derived solitary wave solution, we obtain some special localized excitations and study the interactions between two solitary waves of the system. 相似文献
17.
MA Hong-Cai LOU Sen-Yue 《理论物理通讯》2006,46(6):1005-1010
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. 相似文献
18.
LI Jun-Min DING Wei TANG Xiao-Yan 《理论物理通讯》2007,47(6):1058-1062
We study the symmetries of a (2+1)-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained. 相似文献
19.
Naranmandula HU Jian-Guo BAO Gang Tubuxin 《理论物理通讯》2008,49(5):1109-1113
Using improved homogeneous balance method, we obtain complex function form new exact solutions for the (1+1)-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately. 相似文献
20.
JIA Man LOU Sen-Yue 《理论物理通讯》2006,46(1):91-96
New types of exact solutions of the (N + 1)-dimensional φ^4-model are studied in detail. Some types of interaction solutions such as the periodic-periodic interaction waves and the periodic-solitary wave interaction solutions are found. 相似文献