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1.
Explicit and exact travelling plane wave solutions of the (2+1)—dimensional Boussinesq equation 总被引:1,自引:0,他引:1
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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
2.
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
3.
本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统,成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。 相似文献
4.
BAI Cheng-Lin 《理论物理通讯》2004,41(1):15-20
Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, the nonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of single solitary wave solution and the multisoliton solutions are constructed. 相似文献
5.
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
6.
A simple algebraic transformation relation of a special type of solution between the (3 1)-dimensional Kadomtsev-petviashvili(KP) equation and the cubic nonlinear Klein-Gordon equation (NKG) is established.Using known solutions of the NKG equation,we can obtain many soliton solutions and periodic solution of the (3 1)-dimensional KP equation. 相似文献
7.
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems. 相似文献
8.
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
9.
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixtb-aegree nonnneal term, we study the (2+l )-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations. 相似文献
10.
We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model. 相似文献
11.
Using the extended homogeneous balance method, we find
some special types of single solitary wave solution and new types
of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa
equation. 相似文献
12.
Backlünd transformation and multiple soliton solutions for the (3+1)-dimensional Nizhnik-Novikov-Veselov equation
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We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions. 相似文献
13.
14.
The integrability of the (2+1)-dimensional Broer-Kaup equation with variable coefficients (VCBK) is verified by finding a transformation mapping it to the usual (2+1)-dimensional Broer-Kaup equation (BK). Thus the solutions of the (2+1)-dimensional VCBK are obtained by making full use of the known solutions of the usual (2+1)-dimensional BK. Two new integrable models are given by this transformation, their dromion-like solutions and rogue wave solutions are also obtained. Further, the velocity of the dromion-like solutions can be designed and the center of the rogue wave solutions can be controlled artificially because of the appearance of the four arbitrary functions in the transformation. 相似文献
15.
Variable Separation Solution for (1+1)-Dimensional Nonlinear Models Related to Schroedinger Equation
XUChang-Zhi ZHANGJie-Fang 《理论物理通讯》2004,42(4):568-572
A variable separation approach is proposed and successfully extended to the (1 1)-dimensional physics models. The new exact solution of (1 1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately. 相似文献
16.
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schrödinger (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
17.
The (2+1)-dimensional Konopelchenko-Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the (2+1)-dimensional Konopelchenko-Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is solved by the consistent Riccati expansion (CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the (2+1)-dimensional Konopelchenko-Dubrovsky equation. 相似文献
18.
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the
x-axis. In this paper, with the aid of symbolic computation, six
kinds of new special exact soltion-like solutions of
(2+1)-dimensional breaking soliton equation are obtained by using
some general transformations and the further generalized
projective Riccati equation method. 相似文献
19.
BIAN Xue-Jun 《理论物理通讯》2005,44(5):815-820
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
20.
利用Hirota方法及Riemann theta函数得到了一个(3+1)维孤子方程的周期解.在极限情况下,该周期解退化为孤子解.另外,利用计算机技术和Mathematica绘制了解的三维曲面图. 相似文献