共查询到20条相似文献,搜索用时 78 毫秒
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利用动力系统方法研究一维Tonks-Girardeau原子气区域中Gross-Pitaevskii (GP)方程简化模型的一些精确行波解以及这些精确行波解的动力学行为, 研究系统的参数对行波解的动力学行为的影响. 在不同的参数条件下, 获得了一维Tonks-Girardeau原子气区域中GP方程简化模型的六个行波解的精确参数表达式.
关键词:
动力系统方法
孤立波解
周期波解
扭波解 相似文献
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Chenglin Bai 《Reports on Mathematical Physics》2004,53(2):291-299
A method to construct the new exact solutions of nonlinear partial differential equations (NLPDEs) in a unified way is presented, which is named an improved sine-cosine method. This method is more powerful than the sine-cosine method. Systems of dispersive long wave equations in (1+1) and (2+1) dimensions are chosen to illustrate the method and several types of explicit and exact travelling wave solutions are obtained. These solutions contain Wang's results and other types of solitary wave solutions and new solutions. The method presented here is general and can also be applied to solve more systems of nonlinear partial differential equations, such as the coupled KdV equations. 相似文献
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An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics. 相似文献
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New explicit exact solutions for a generalized Hirota—Satsuma coupled KdV system and a coupled MKdV equation 总被引:7,自引:0,他引:7 下载免费PDF全文
In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained. 相似文献
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New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients
CHEN Huai-Tang ZHANG Hong-Qing 《理论物理通讯》2004,42(10)
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3 1 )-dimensional Burgers equation with variable coefficients. 相似文献
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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
10.
New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients 总被引:1,自引:0,他引:1
CHENHuai-Tang ZHANGHong-Qing 《理论物理通讯》2004,42(4):497-500
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3 1)-dimensional Burgers equation with variable coefficients. 相似文献
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A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation 下载免费PDF全文
A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein-Gordon equation. 相似文献
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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
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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
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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.
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
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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
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ZHU Jia-Min LU Zhi-Ming LIU Yu-Lu 《理论物理通讯》2008,49(6):1403-1406
One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions. 相似文献
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With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition. 相似文献
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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
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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