共查询到20条相似文献,搜索用时 31 毫秒
1.
O.P. Layeni 《Applied mathematics and computation》2009,215(8):2901-2907
A new rational auxiliary equation method for obtaining exact traveling wave solutions of constant coefficient nonlinear partial differential equations of evolution is proposed. Its effectiveness is evinced by obtaining exact solutions of a generalized Zakharov system, some of which are new. It is shown that the G′/G and the generalized projective Ricatti expansion methods are special cases of the auxiliary equation method. Further, due the solutions obtained, four other new and practicable rational methods are deduced. 相似文献
2.
M. A. Abdou 《Numerical Methods for Partial Differential Equations》2010,26(5):993-1005
With the aid of computer symbolic computation system Maple, the generalized auxiliary equation method is first applied to two nonlinear evolution equations, namely, the nonlinear elastic rod equation and (2 + 1)‐dimensional Boiti‐Leon‐Pempinelli equation. As a results, some new types of exact traveling wave solutions are obtained which include bell and kink profile solitary wave solutions, and triangular periodic wave solutions and singular solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
3.
4.
施业琼 《数学的实践与认识》2009,39(16)
分析研究了一个具有三次增益效应和五次耗散项的2+1维Ginzburg-Landau方程.利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解. 相似文献
5.
An analytic technique, the homotopy analysis method (HAM), is applied to solve the generalized Benjamin–Bona–Mahony (BBM)
equation. An explicit series solution is given, different from traditional analytic techniques, our approach is independent
of knowing some parameters. This analytic method provides us with a new way to obtain series solutions of such problems. The
homotopy analysis method contains the auxiliary parameter ħ, which provides us with a simple way to adjust and control the convergence region of series solution. 相似文献
6.
We obtain new exact solutions to generalized Sawada-Kotera equation. Using the variational iteration method combined with the improved generalized tanh-coth method, we construct new traveling wave solutions for the standard Sawada-Kotera equation and, by means of scaling, we obtain new solutions to general Sawada-Kotera equation. Periodic and soliton solutions are formally derived for both models. 相似文献
7.
A new special two-soliton solution to the generalized Sine–Gordon equation with a variable coefficient is constructed analytically, by using the self-similar method and Hirota bilinear method. To construct this special solution, we do not utilize the pairs of one-soliton solutions, as is customarily done when solving the Sine–Gordon equation, but introduce two auxiliary self-similar variables in Hirota’s procedure. We also study features of this solution by choosing different self-similar variables. The results obtained confirm that the behavior of such Sine–Gordon solitons can be easily controlled by the selection of the self-similar variables. 相似文献
8.
In this paper, a series of abundant exact travelling wave solutions is established for a modified generalized Vakhnenko equation by using auxiliary equation method. These solutions can be expressed by Jacobi elliptic function. When Jacobi elliptic functions modulus m→1 or 0, the travelling wave solutions degenerate to four types of solutions, namely, the soliton solutions, the hyperbolic function solutions, the trigonometric function solutions, constant solutions. 相似文献
9.
本文研究了Fisher方程和Burgers-Fisher方程.运用一种辅助微分方程方法,得到了这两种非线性偏微分方程新的精确行波解. 相似文献
10.
By employing auxiliary equation method and Hirota bilinear method, the quantum Zakharov-Kuznetsov equation which arises in quantum magnetoplasma is investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of multidimensional nonlinear ion-acoustic waves in dense magnetoplasma. 相似文献
11.
12.
By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions are obtained with the aid of symbolic computation. 相似文献
13.
In this letter, a new auxiliary function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of the solutions of the elliptic equation to construct exact travelling wave solutions of nonlinear partial differential equations. More new exact travelling wave solutions are obtained for the generalized coupled Hirota–Satsuma KdV system. 相似文献
14.
In this paper,auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation.We study the(2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions.The method used here can be also extended to other nonlinear partial differential equations. 相似文献
15.
Cesar A. Gomez Sierra 《Applied mathematics and computation》2010,216(1):357-2972
The generalized tanh-coth method is used to construct periodic and soliton solutions for a new integrable system, which has been derived from an integrable sixth-order nonlinear wave equation (KdV6). The system is formed by two equations. One of the equations may be considered as a Korteweg-de Vries equation with a source and the second equation is a third-order linear differential equation. 相似文献
16.
Based on the homogeneous balance method,the Jacobi elliptic expansion method and the auxiliary equation method,the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations.New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple.The method is also valid for other (1+1)-dimensional and higher dimensional systems. 相似文献
17.
In this paper, we establish new solitary wave solutions to the modified Kawahara equation by the sine-cosine method. Moreover, the periodic solutions and bell-shaped solitons solutions to the generalized fifth-order KdV equation are obtained. The tanh method is used to handle the double sine-Gordon equation and the double sinh-Gordon equation. Families of exact travelling wave solutions are formally derived. The rational triangle sine-cosine method is introduced and to be constructed complex solutions to the modified Degasperis-Procesi (DP) equation and the modified Camassa-Holm (CH) equation. 相似文献
18.
Based on the computerized symbolic, a new generalized tanh functions method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (PDES) in a unified way. The main idea of our method is to take full advantage of an auxiliary ordinary differential equation which has more new solutions. At the same time, we present a more general transformation, which is a generalized method for finding more types of travelling wave solutions of nonlinear evolution equations (NLEEs). More new exact travelling wave solutions to two nonlinear systems are explicitly obtained. 相似文献
19.
S. Abbasbandy E. Babolian M. Ashtiani 《Communications in Nonlinear Science & Numerical Simulation》2009,14(12):4114-4121
In this paper, an analytic technique, namely the homotopy analysis method (HAM) is applied to obtain approximations to the analytic solution of the generalized Zakharov equation. The HAM contains the auxiliary parameter , which provides us with a simple way to adjust and control the convergence region of the solution series. 相似文献
20.
Zitian Li 《Applied mathematics and computation》2009,215(8):2886-2890
In this short letter, new exact solutions including kink solutions, soliton-like solutions and periodic form solutions for a combined version of the potential KdV equation and the Schwarzian KdV equation are obtained using the generalized Riccati equation mapping method. 相似文献