共查询到20条相似文献,搜索用时 11 毫秒
1.
利用符号计算软件Maple,在一个新的广义的Riccati方程有理展开法的帮助下,得到了关于复合的KdV系统及广义的KdV-Burgers系统的几个新的更广义类型的精确解.该方法还可被应用到其他非线性发展方程中去. 相似文献
2.
The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics
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Using the projective Riccati equation expansion (PREE) method, new
families of variable separation solutions (including solitary wave
solutions, periodic wave solutions and rational function solutions)
with arbitrary functions for two nonlinear physical models are
obtained. Based on one of the variable separation solutions and by
choosing appropriate functions, new types of interactions between
the multi-valued and single-valued solitons, such as a peakon-like
semi-foldon and a peakon, a compacton-like semi-foldon and a
compacton, are investigated. 相似文献
3.
Symbolic Computation and Construction of Soliton-Like Solutions to the(2+1)-Dimensional Breaking Soliton Equation 总被引:2,自引:0,他引:2
Based on the computerized symbolic system Maple, a new generalized expansion method of Riccatiequation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new generalansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = 0, uy = vx, and obtain rich new families of the exact solutions of the breaking soliton equation, including thenon-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular functionsolutions. 相似文献
4.
CHENYong LIBiao ZHANGHong-Qing 《理论物理通讯》2003,40(2):137-142
Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions. 相似文献
5.
6.
<正>To seek new infinite sequence of exact solutions to nonlinear evolution equations,this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation.Based on the tanhfunction expansion method and homogenous balance method,new infinite sequence of exact solutions to Zakharov-Kuznetsov equation,Karamoto-Sivashinsky equation and the set of(2+l)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica.The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations. 相似文献
7.
A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary function of an independent variable.Based on the solution,two hyperbolic functions are chosen to construct new solitons.Novel single-loop-like and double-loop-like solitons are found for the equation. 相似文献
8.
A nontraveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation. 相似文献
9.
The residual symmetry of the generalized Kaup-Kupershmidt(gKK) equation is obtained from the truncated Painlevé expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Furthermore, the g KK equation is proved to integrable in the sense of owning consistent Riccati expansion and some new B¨acklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given. 相似文献
10.
By means of generalized Riccati equation expansion method and symbolic computation, some exact analytical solutions, which contain soliton-like solutions and periodic-like solutions to the generalized Calogero-Bogoyavlenskii-Schiff (GCBS) equation, are obtained. From our results, the solitary-wave solutions and previously known soliton-like solutions of the special cases of GCBS equation can be recovered. 相似文献
11.
LIU Xiao-Ping LIU Chun-Ping 《理论物理通讯》2007,48(4):610-614
In this paper, some solutions of a generalized Riccati equation are investigated, which are given in the recent articles [Chaos, Solitons & Fractals 24 (2005) 257; Phys. Lett. A 336 (2005) 463], and the relationship among the solutions is revealed. 相似文献
12.
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
13.
In this paper, we consider an extended Korteweg-de Vries (KdV) equation. Using the consistent Riccati expansion (CRE) method of Lou, the extended KdV equation is proved to be CRE solvable in only two distinct cases. These two CRE solvable models are the KdV-Lax and KdV-Sawada-Kotera (KdV-SK) equations. In addition, applying the nonauto-Bäcklund transformations which are provided by the CRE method, we present the explicit construction for soliton-cnoidal wave interaction solutions which represent a soliton propagating on a cnoidal periodic wave background in the KdV-Lax and KdV-SK equations, respectively. 相似文献
14.
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
15.
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
16.
17.
Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the
exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the (2+1)-dimentional breaking soliton
equation. As a result, we successfully obtain some new and more general
solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sample, the properties of some soliton solutions for the breaking soliton equation are shown by some
figures. Our method can also be applied to other partial differential equations. 相似文献
18.
采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解.
关键词:
(3+1)维Nizhnik-Novikov-Veselov方程
非线性Klein-Gordon方程
孤子解
周期解 相似文献
19.
By applying the bifurcation theory of dynamical system to the generalized KP-BBM equation, the phase portraits of the travelling
wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth
periodic waves converge to periodic cusp waves. Under different parametric conditions, various sufficient conditions to guarantee
the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are obtained.
相似文献
20.
A class of generalized Vakhnemko equation is considered.
First, we solve the nonlinear differential equation by the homotopic
mapping method. Then, an approximate soliton solution for
the original generalized Vakhnemko equation is obtained. By this method
an arbitrary order approximation can be easily obtained and,
similarly, approximate soliton solutions of other nonlinear
equations can be acquired. 相似文献