共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, based on a new system of three Riccati equations, we give a new method to construct more new exact solutions of nonlinear differential equations in mathematical physics. The classical Boussinesq system is chosen to illustrate our method. As a consequence, more families of new exact solutions are obtained, which include solitary wave solutions and periodic solutions. 相似文献
2.
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively. 相似文献
3.
WANG Yue-Ming LI Xiang-Zheng YANG Sen WANG Ming-Liang 《理论物理通讯》2005,44(3):396-400
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively. 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.
Based on a known transform, the exact solutions of (2 1)-dimensional Broer-Kaup equations are inves tigated by using the method of direct integral. A kind of new exact solutions of Broer-Kaup equations are obtained, which contain previous results about solitary wave solutions. 相似文献
6.
We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure. 相似文献
7.
LIUGuan-Ting FANTian-You 《理论物理通讯》2004,42(4):488-490
Based on a known transform, the exact solutions of (2 1)-dimensional Broer-Kaup equations are investigated by using the method of direct integral. A kind of new exact solutions of Broer Kaup equations are obtained,which contain previous results about solitary wave solutions. 相似文献
8.
For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. 相似文献
9.
References: 《理论物理通讯》2007,48(7):7-10
Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations. 相似文献
10.
Based on the generalized Riccati relation, an algebraic method
to construct a series of exact solutions to nonlinear evolution
equations is proposed. Being concise and straightforward, the method
is applied to Maccari's system, and some exact solutions of the system
are obtained. The method is of important significance in exploring
exact solutions for other nonlinear evolution equations. 相似文献
11.
Some new exact travelling wave and period solutions of
discrete nonlinear Schrödinger equation are found
by using a hyperbolic tangent function approach, which was usually
presented to find exact travelling wave solutions of certain
nonlinear partial differential models. Now we can further extend
the new algorithm to other nonlinear differential-different models. 相似文献
12.
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
13.
Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz‘s conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.`` 相似文献
14.
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained. 相似文献
15.
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
16.
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
17.
A New Approach to Solve Nonlinear Wave Equations 总被引:3,自引:0,他引:3
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions. 相似文献
18.
HUANG Shou-Jun CHEN Chun-Li 《理论物理通讯》2007,48(5):773-780
In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated. 相似文献
19.
A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation 总被引:1,自引:0,他引:1
YANG Zong-Hang 《理论物理通讯》2006,46(11)
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 guideline to classify the various types of the solution according to some parameters. 相似文献
20.
In cylindrical coordinate, exact wave functions
of the two-dimensional time-dependent harmonic oscillator in
a time-dependent magnetic field are derived by using the trial
function method. Meanwhile, the exact classical solution as well
as the classical phase is obtained too. Through the Heisenberg
correspondence principle, the quantum solution and the classical
solution are connected together. 相似文献