共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Nikolay A. Kudryashov 《Applied mathematics and computation》2010,217(5):2282-2284
Exact solutions of the (2+1)-dimensional Kadomtsev-Petviashvili by Zhang [Huiqun Zhang, A note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Appl. Math. Comput. 216 (2010) 2771-2777] are considered. To look for “new types of exact solutions travelling wave solutions” of equation Zhang has used the G′/G-expansion method. We demonstrate that there is the general solution for the reduction by Zhang from the (2+1)-dimensional Kadomtsev-Petviashvili equation and all solutions by Zhang are found as partial cases from the general solution. 相似文献
4.
Comment on “New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”
Nikolai A. Kudryashov Pavel N. RyabovDmitry I. Sinelshchikov 《Journal of Computational and Applied Mathematics》2011,235(15):4513-4515
In this comment we analyze the paper [Abdelhalim Ebaid, S.M. Khaled, New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity, J. Comput. Appl. Math. 235 (2011) 1984-1992]. Using the traveling wave, Ebaid and Khaled have found “new types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”. We demonstrate that the authors studied the well-known nonlinear ordinary differential equation with the well-known general solution. We illustrate that Ebaid and Khaled have looked for some exact solution for the reduction of the nonlinear Schrodinger equation taking the general solution of the same equation into account. 相似文献
5.
The purpose of this paper is to reveal the dynamical behavior of the nonlinear wave equation with fifth-order nonlinear term, and provides its bounded traveling wave solutions. Applying the bifurcation theory of planar dynamical systems, we depict phase portraits of the traveling wave system corresponding to this equation under various parameter conditions. Through discussing the bifurcation of phase portraits, we obtain all explicit expressions of solitary wave solutions and kink wave solutions. Further, we investigate the relation between the bounded orbit of the traveling wave system and the energy level h. By analyzing the energy level constant h, we get all possible periodic wave solutions. 相似文献
6.
Lazhar Bougoffa 《Applied mathematics and computation》2010,216(2):689-8913
The Abel equation of the second kind
[g0(x)+g1(x)u]u′=f0(x)+f1(x)u+f2(x)u2 相似文献
7.
Elsayed M.E. Zayed 《Applied mathematics and computation》2011,218(7):3962-3964
Jawad et al. have applied the modified simple equation method to find the exact solutions of the nonlinear Fitzhugh-Naguma equation and the nonlinear Sharma-Tasso-Olver equation. The analysis of the Sharma-Tasso-Olver equation obtained by Jawad et al. is based on variant of the modified simple equation method. In this paper, we provide its direct application and obtain new 1- soliton solutions. 相似文献
8.
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in n>1 dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of similarity variables given by group foliations of this heat equation, using its admitted group of scaling symmetries. This technique yields explicit similarity solutions as well as other explicit solutions of a more general (non-similarity) form having interesting analytical behavior connected with blow up and dispersion. In contrast, standard similarity reduction of this heat equation gives a semilinear ODE that cannot be explicitly solved by familiar integration techniques such as point symmetry reduction or integrating factors. 相似文献
9.
Aly R. Seadawy 《Applied Mathematics Letters》2012,25(4):687-691
In the present study, we converted the resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrödinger (NLS) equation. Applying the function transformation method, the NLS equation was transformed to an ordinary differential equation, which depended only on one function ξ and can be solved. The general solution of the latter equation in ζ leads to a general solution of NLS equation. A new set of exact solutions for the two-dimensional NLS equation is obtained. 相似文献
10.
非线性偏微分方程的约化和精确解 总被引:3,自引:0,他引:3
§ 1 IntroductionSeeking the exact solutions of the nonlinear partial differential equation is one of thevery importantsubjectin PDE research.Up to now,many methods offinding the exact so-lutions for NLPDE are constructed,such as inverse scattering transformation(IST) [1 ] ,Liepoint symmetry and similar reductions[2 ,3] ,B cklund[4— 6] and Cole-Hofe transformations,Hirota s bilinear method[7] ,the homogeneous balance method[8,9] ,tanh function method[1 0 ]and so on.In this paper,we giv… 相似文献
11.
Hong Zhao 《Applied mathematics and computation》2010,216(4):1219-479
This paper presents a new algebraic procedure to construct exact solutions of selected nonlinear differential-difference equations. The discrete sine-Gordon equation and differential-difference asymmetric Nizhnik-Novikov-Veselov equations are chosen as examples to illustrate the efficiency and effectiveness of the new procedure, where various types of exact travelling wave solutions for these nonlinear differential-difference equations have been constructed. It is anticipated that the new procedure can also be used to produce solutions for other nonlinear differential-difference equations. 相似文献
12.
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
13.
Ibrahim E. Inan 《Applied mathematics and computation》2010,217(4):1294-1299
In this paper, we implemented the exp-function method for the exact solutions of the fifth order KdV equation and modified Burgers equation. By using this scheme, we found some exact solutions of the above-mentioned equations. 相似文献
14.
Painlevé analysis and exact solutions of the nonlinear diffusion equation with a polynomial source 下载免费PDF全文
Nikolay A. Kudryashov Ilya Y. Gaiur 《Mathematical Methods in the Applied Sciences》2016,39(3):488-497
Nonlinear diffusion equation with a polynomial source is considered. The Painlevé analysis of equation has been studied. Exact traveling wave solutions in the simplest cases have been found. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
15.
This paper is concerned with a nonlinear iterative functional differential equation x′(z) = 1/x(p(z) + bx′(z)). By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. We discuss not only in the general case, but also in critical cases, especially for α given in Schröder transformation is a root of the unity. And in case (H4), we dealt with the equation under the Brjuno condition, which is weaker than the Diophantine condition. Moreover, the exact and explicit solution of the original equation has been investigated for the first time. Such equations are important in both applications and the theory of iterations. 相似文献
16.
Mohamed Hayek 《Applied mathematics and computation》2011,218(6):2407-2420
Based on the simplest equation method, we propose exact and traveling-wave solutions for a nonlinear convection-diffusion-reaction equation with power law nonlinearity. Such equation can be considered as a generalization of the Fisher equation and other well-known convection-diffusion-reaction equations. Two important cases are considered. The case of density-independent diffusion and the case of density-dependent diffusion. When the parameters of the equation are constant, the Bernoulli equation is used as the simplest equation. This leads to new traveling-wave solutions. Moreover, some wavefront solutions can be derived from the traveling-wave ones. The case of time-dependent velocity in the convection term is studied also. We derive exact solutions of the equations by using the Riccati equation as simplest equation. The exact and traveling-wave solutions presented in this paper can be used to explain many biological and physical phenomena. 相似文献
17.
Thierry Cazenave Flvio Dickstein Fred B. Weissler 《Journal of Mathematical Analysis and Applications》2009,360(2):537-547
In this paper, we consider the nonlinear heat equation(NLH)
ut−Δu=|u|αu,