共查询到20条相似文献,搜索用时 15 毫秒
1.
《Physics letters. A》2006,358(4):275-282
The extended mapping method with a computerized symbolic computation is used to drive some new exact solutions of four nonlinear evolution equations in mathematical physics. As a result, many exact travelling wave solutions are obtained which include new solitary wave solutions, triangular and hyperbolic functions. Solutions in the limiting cases have also been studied. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. 相似文献
2.
Sheng Zhang 《Physics letters. A》2008,372(11):1873-1880
In this Letter, the Exp-function method is used to seek generalized solitonary solutions of Riccati equation. Based on the Riccati equation and its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations in mathematical physics. 相似文献
3.
In terms of the solutions of the generalized Riccati equation,
a new algebraic method, which contains the terms of radical expression of functions f(ξ), is constructed to explore
the new exact solutions for nonlinear evolution equations.
Being concise and straightforward, the method is applied to
nonlinear Klein-Gordon equation, and some new 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
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5.
In this Letter, a variable-coefficient extended mapping method is proposed to seek new and more general exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients and (2+1)-dimensional Nizhnik-Novikov-Veselov equations. As a result, many new and more general exact solutions are obtained including Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear evolution equations in mathematical physics. 相似文献
6.
In terms of the solutions of an auxiliary ordinary differential
equation, a new algebraic method, which contains the terms of first-order
derivative of functions f(ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations. 相似文献
7.
Jun-ting Pan 《Physics letters. A》2009,373(35):3118-3121
A new auxiliary equation method, constructed by a first order nonlinear ordinary differential equation with at most an eighth-degree nonlinear term, is first proposed for exploring more exact solutions to nonlinear evolution equations. Being concise and straightforward, the method, with the aid of symbolic computation, is applied to the Sharma-Tasso-Olver model, and some new exact solitary wave solutions are obtained. The approach is also applicable to searches for exact solutions of other nonlinear evolution equations. 相似文献
8.
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
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
9.
In this Letter, a new kind of Lamé functions are given. Based on the new Lamé functions and Jacobi elliptic function, the perturbation method is applied to the nonlinear equations, and many multi-order solutions of novel forms are derived. In addition, it is shown that different Lamé functions can exist in the first order solutions of nonlinear system. 相似文献
10.
利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程,应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.
关键词:
Jacobi椭圆函数
Lam函数
多级准确解
非线性演化方程
扰动方法 相似文献
11.
WU Guo-Jiang HAN Jia-Hua ZHANG Wen-Liang ZHANG Miao WANG Jun-Mao 《理论物理通讯》2007,48(5):815-818
By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations. 相似文献
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13.
SHEN Shou-Feng 《理论物理通讯》2006,45(2):236-238
By means of the variable separation method, new exact solutions of some (1+1)-dimensional nonlinear evolution
equations are obtained. Abundant localized excitations can be
found by selecting corresponding arbitrary functions
appropriately. Namely, the new soliton-like localized excitations
and instanton-like localized excitations are presented. 相似文献
14.
ZHANG Xiao-Ling WANG Jing ZHANG Hong-Qing 《理论物理通讯》2006,46(5):779-786
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order. 相似文献
15.
In this paper, based on a new more general ansatz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order. 相似文献
16.
There are many interesting methods can be utilized to construct special solutions of nonlinear differential equations with constant coefficients. However, most of these methods are not applicable to nonlinear differential equations with variable coefficients. A new method is presented in this Letter, which can be used to find special solutions of nonlinear differential equations with variable coefficients. This method is based on seeking appropriate Bernoulli equation corresponding to the equation studied. Many well-known equations are chosen to illustrate the application of this method. 相似文献
17.
扩展齐次平衡法与Backlund变换 总被引:1,自引:0,他引:1
将求解非线性演化方程的齐次平衡法进行了扩展,使其包含一个任意函数.此改进方法可得到耦合KdV-Burgers方程、KdV-Burgers方程、Boussinesq方程和一般KdV方程等许多非线性演化方程的Backlund变换和新的精确解. 相似文献
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19.
In this work, we present travelling wave solutions for the Burgers, Burgers–Huxley and modified Burgers–KdV equations. The (G′/G)-expansion method is used to determine travelling wave solutions of these sets of equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. 相似文献
20.
HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(2):171-174
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献