共查询到20条相似文献,搜索用时 6 毫秒
1.
《Chaos, solitons, and fractals》2004,19(1):147-150
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact travelling wave solutions for nonlinear evolution equations. By this method the Kawahara and the modified Kawahara equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation. 相似文献
2.
K. R. Schneider E. A. Shchepakina V. A. Sobolev 《Mathematical Methods in the Applied Sciences》2003,26(16):1349-1361
We study the existence of combustion waves for an autocatalytic reaction in the non‐adiabatic case. Based on the fact that the reaction system has canard solutions separating the slow combustion regime from the explosive one, we prove by applying the geometric theory of singularly perturbed differential equations the existence of a new type of travelling waves solutions, the so‐called canard travelling waves. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
3.
Xijun Deng 《Applied mathematics and computation》2011,218(5):2269-2276
Exact solutions for the modified Camassa-Holm and Degasperis-Procesi equations by Liu et al. (2010) [Y.F. Liu, X.Y. Zhu, J.X. He, Factorization technique and new exact solutions for the modified Camassa-Holm and Degasperis-Procesi equations, Appl. Math. Comput. 217 (2010) 1658-1665] are investigated. Liu et al. has used the factorization technique to reduce the modified Camassa-Holm and Degasperis-Procesi equations to first-order ordinary differential equations, and then derived some exact travelling wave solutions by direct integral method. In this note, we will explain that the implementation of the so-called factorization technique is completely unnecessary. Moreover, based on the method of complete discrimination system for polynomial, we shall demonstrate that the general explicit exact solution and its classification for the above two types of equations can be obtained directly and many exact solutions by Liu et al. are our special cases. Besides, some known results in previously relevant literatures are extended and some simple remarks are also made. 相似文献
4.
Gambo Betchewe Bouetou Bouetou Thomas Kuetche Kamgang Victor Kofane Timoleon Crepin 《Applied mathematics and computation》2010,217(1):203-211
We investigate the dynamical behavior of a generalized-Zakharov equation for the complex envelope of the high-frequency wave and the real low-frequency field by analyzing its phase portraits. Following a dynamical system approach, in different parameter regions, we depict phase portraits of a travelling wave system. Through discussing the bifurcation of phase portraits, we unwrap explicit miscellaneous travelling waves including localized and periodic ones. 相似文献
5.
In this work we develop a variety of Burgers-like equations. We show that these derived equations share some of the travelling wave solutions of the Burgers equation, and differ in some other solutions. 相似文献
6.
This study is carried out to investigate the numerical solutions of the Kawahara, KdV‐Kawahara, and the modified Kawahara equations by using the meshless method based on collocation with radial basis functions. Results of the meshless method with different radial basis functions are presented for the travelling wave solution of the Kawahara type equations. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 542–553, 2012 相似文献
7.
Ahmet Bekir 《Communications in Nonlinear Science & Numerical Simulation》2009,14(4):1069-1077
In this paper, we establish exact solutions for complex nonlinear equations. The tanh–coth and the sine–cosine methods are used to construct exact periodic and soliton solutions of these equations. Many new families of exact travelling wave solutions of the coupled Higgs and Maccari equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems. 相似文献
8.
Sirendaoreji 《高校应用数学学报(英文版)》2004,19(2):178-186
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation. 相似文献
9.
研究高阶Camassa-Holm方程的行波解,采用一种新的方法求解行波方程,获得了高阶Camassa-Holm方程的一类行波解. 相似文献
10.
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
11.
By using new solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact travelling wave solutions for nonlinear evolution equation. By this method some nonlinear evolution equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation. 相似文献
12.
Nikolai A. Kudryashov 《Journal of Computational and Applied Mathematics》2010,234(12):3511-3512
Exact solutions of the Kawahara equation by Assas [L.M.B. Assas, New Exact solutions for the Kawahara equation using Exp-function method, J. Comput. Appl. Math. 233 (2009) 97-102] are analyzed. It is shown that all solutions do not satisfy the Kawahara equation and consequently all nontrivial solutions by Assas are wrong. 相似文献
13.
Filipe J. Romeiras 《Applied mathematics and computation》2009,215(5):1791-1805
We search for exact travelling wave solutions of the generalized Bretherton equation for integer, greater than one, values of the exponent m of the nonlinear term by two methods: the truncated Painlevé expansion method and an algebraic method. We find periodic solutions for m=2 and m=5, to add to those already known for m=3; in all three cases these solutions exist for finite intervals of the wave velocity. We also find a “kink” shaped solitary wave for m=5 and a family of elementary unbounded solutions for arbitrary m. 相似文献
14.
Zhang Ping 《Applied mathematics and computation》2010,217(4):1688-1696
In this paper, by using the improved Riccati equations method, we obtain several types of exact traveling wave solutions of breaking soliton equations and Whitham-Broer-Kaup equations. These explicit exact solutions contain solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions. The method employed here can also be applied to solve more nonlinear evolution equations. 相似文献
15.
In this paper, an improved tanh function method is used with a computerized symbolic computation for constructing new exact travelling wave solutions on two nonlinear physical models namely, the quantum Zakharov equations and the (2+1)-dimensional Broer–Kaup–Kupershmidt (BKK) system. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions.The exact solutions are obtained which include new soliton-like solutions, trigonometric function solutions and rational solutions. The method is straightforward and concise, and its applications are promising. 相似文献
16.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(9):1776-1781
By using some exact solutions of an auxiliary ordinary differential equation, a new direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the complex coupled KdV equations and modified KdV equation. New exact complex solutions are obtained. 相似文献
17.
运用了tanh-coth展开法,得到了Benny-Luke方程和Phi-4方程的一些新的精确行波解。同时该方法也可用于其他的非线性演化方程。 相似文献
18.
《Chaos, solitons, and fractals》2007,31(4):840-852
Based on computerized symbolic computation and modified extended tanh-function method for constructing a new exact travelling wave solutions of nonlinear evolution equations (NEEs) is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some (NEEs) with mathematical physics interests. As a results, we can successfully recover the previously known solitary wave solutions that had been found by the tanh-function method and other more sophisticated methods. 相似文献
19.
D. G. Natsis 《Numerical Algorithms》2007,44(3):281-289
In this paper we derive an analytical solution of the one-dimensional Boussinesq equations, in the case of waves relatively
long, with small amplitudes, in water of varying depth. To derive the analytical solution we first assume that the solution
of the model has a prescribed wave form, and then we obtain the wave velocity, the wave number and the wave amplitude. Finally
a specific application for some realistic values of wave parameters is given and a graphical presentation of the results is
provided.
相似文献
20.
We present an alternative functional variable method or briefly called FVM (in short) to analyze a class of wave equations, consisting in construction of exact travelling solutions. Some important nonlinear model equations which arise in a wide variety of physical problems have been presented as testbed to show the application of this method. 相似文献