共查询到20条相似文献,搜索用时 15 毫秒
1.
ZHENG Chun-Long FEI Jin-Xi 《理论物理通讯》2007,48(4):657-661
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions (including solltary wave solutlons, periodic wave solutions and rational function solutions) with arbitrary functions [or the (2+ 1)-dimensional general/zed Broer-Kaup (GBK) system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the (2+1)-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed. 相似文献
2.
In the present letter, we get the appropriate bilinear forms of(2+1)-dimensional KdV equation, extended (2+1)-dimensional shallow water wave equation and (2+1)-dimensional Sawada-Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions. 相似文献
3.
In this paper,the generalized Boussinesq wave equation u tt-uxx+a(um) xx+buxxxx=0 is investigated by using the bifurcation theory and the method of phase portraits analysis.Under the different parameter conditions,the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. 相似文献
4.
A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation. 相似文献
5.
Carsten Blank Martina Chirilus-Bruckner Vincent Lescarret Guido Schneider 《Communications in Mathematical Physics》2011,302(3):815-841
For nonlinear wave equations existence proofs for breathers are very rare. In the spatially homogeneous case up to rescaling the sine-Gordon equation \({\partial^2_t u = \partial^2_x u - \sin (u)}\) is the only nonlinear wave equation which is known to possess breather solutions. For nonlinear wave equations in periodic media no examples of breather solutions have been known so far. Using spatial dynamics, center manifold theory and bifurcation theory for periodic systems we construct for the first time such time periodic solutions of finite energy for a nonlinear wave equationwith spatially periodic coefficients s, q, and r on the real axis. Such breather solutions play an important role in theoretical scenarios where photonic crystals are used as optical storage.
相似文献
$ s(x) \partial^2_t u(x,t) = \partial^2_x u(x,t) - q(x) u(x,t)+ r(x)u(x,t)^3, $
6.
Z. J. Yang R. A. Dunlap D. J. W. Geldart 《International Journal of Theoretical Physics》1994,33(10):2057-2065
By the introduction of some ansatz equations, we have obtained several new classes of traveling (solitary) wave solutions to the nonlinear diffusion equation $$f_1 (u)u_t + f_2 (u)u_x + f_3 (u)u_{xx} + f_4 (u)u_x^2 = f_5 (u)$$ and the nonlinear wave equation $$f_1 (u)u_u + f_2 (u)u_t + f_3 (u)u_{xx} + f_4 (u)u_x + f_5 (u)u_x^2 + \cdots = f_6 (u)$$ Some applications of these solutions are discussed. 相似文献
7.
Explicit and exact travelling plane wave solutions of the (2+1)—dimensional Boussinesq equation 总被引:1,自引:0,他引:1
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
The deformation mapping method is applied to solve a system of (2+1)-dimensional Boussinesq equations. Many types of explicit and exact travelling plane wave solutions, which contain solitary wave solutions,periodic wave solutions,Jacobian elliptic function solutions and others exact solutions, are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and the cubic nonlinear Klein-Gordon equation. 相似文献
8.
Sen Yue Lou Man Jia Fei Huang Xiao Yan Tang 《International Journal of Theoretical Physics》2007,46(8):2082-2095
Some simple special Bäcklund transformation theorems are proposed and utilized to obtain exact solutions for the (2+1)-dimensional Euler equation. It is found that the (2+1)-dimensional Euler equation possesses abundant soliton or solitary wave structures, conoid periodic wave structures and the quasi-periodic Bessel wave structures on account of the arbitrary functions in its solutions. Moreover, all solutions of the arbitrary two dimensional nonlinear Poisson equation can be used to construct exact solutions of the (2+1)-dimensional Euler equation. 相似文献
9.
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
10.
QU Gai-Zhu ZHANG Shun-Li ZHU Chun-Rong 《理论物理通讯》2008,49(5):1119-1124
The invariant sets and exact solutions of the (1 + 2)-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u : ux = vxF(u),uy = vyF(u) }. This approach is also developed to solve (1 + N)-dimensional wave equations. 相似文献
11.
New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 总被引:1,自引:0,他引:1
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
12.
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
13.
ZHANGJin-liang WANGMing-liang FANGZong-de 《原子与分子物理学报》2004,21(1):78-82
By using the extended F-expansion method,the exact solutions,including periodic wave solutions expressed by Jaeobi elliptic functions,for (2 1)-dimensional nonlinear Schroedinger 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
14.
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
15.
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
16.
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions. 相似文献
17.
New exact solutions expressed by the Jacobi elliptic
functions are obtained to the (2+1)-dimensional dispersive long-wave
equations by using the modified F-expansion method. In the limit case, new
solitary wave solutions and triangular periodic wave solutions are obtained
as well. 相似文献
18.
C. Eugene Wayne 《Communications in Mathematical Physics》1990,127(3):479-528
In this paper the nonlinear wave equation $$u_u - u_{xx} + v(x)u(x,t) + \varepsilon u^3 (x,t) = 0$$ is studied. It is shown that for a large class of potentials,v(x), one can use KAM methods to construct periodic and quasi-periodic solutions (in time) for this equation. 相似文献
19.
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
20.
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations. 相似文献