共查询到20条相似文献,搜索用时 46 毫秒
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The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves. 相似文献
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?smail Aslan 《Applied mathematics and computation》2009,215(8):3140-3147
We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. Discrete soliton and periodic wave solutions with more arbitrary parameters, as well as discrete rational wave solutions, are revealed. It seems that the utilized method can provide highly accurate discrete exact solutions to NDDEs arising in applied mathematical and physical sciences. 相似文献
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Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method
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Elsayed M. E. Zayed & K. A. E. Alurrfi 《偏微分方程(英文版)》2015,28(4):332-357
The propagation of the optical solitons is usually governed by the nonlinear Schrödinger equations. In this article, the two variable (G'/G, 1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear Schrödinger equations describing the propagation of femtosecond pulses in nonlinear optical fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. Thismethod can be thought of as the generalization of well-known original (G'/G)-expansion method proposed by M. Wang et al. It is shown that the two variable (G'/G, 1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics. 相似文献
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A Generalized (G'/G)-Expansion Method to Find the Traveling Wave Solutions of Nonlinear Evolution Equations
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In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical Boussinesq equations, by using a generalized (G'/G)-expansion method, where G satisfies the Jacobi elliptic equation. Many exact solutions in terms of Jacobi elliptic functions are obtained. 相似文献
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利用推广的(G′/G)展开法,借助于计算机代数系统Mathematica,获得了(2+1)维BBM方程的丰富的显式行波解,分别以含两个任意参数的双曲函数、三角函数及有理函数表示. 相似文献
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利用改进的(G′/G)-展开法,求广义的(2+1)维Boussinesq方程的精确解,得到了该方程含有较多任意参数的用双曲函数、三角函数和有理函数表示的精确解,当双曲函数表示的行波解中参数取特殊值时,便得到广义的(2+1)维Boussinesq方程的孤立波解. 相似文献
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In this paper, we modified the so-called generalized (G′/G)-expansion method to obtain new traveling wave solutions for nonlinear
differential equations. The generalized Zakharov equations are chosen to illustrate the method in detail. 相似文献
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E. M. E. Zayed 《Journal of Applied Mathematics and Computing》2009,30(1-2):89-103
In the present paper, we construct the traveling wave solutions involving parameters for some nonlinear evolution equations in the mathematical physics via the (2+1)-dimensional Painlevé integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Vesselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations by using a new approach, namely the ( $\frac{G'}{G})$ -expansion method, where G=G(ξ) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions. 相似文献
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Huiqun Zhang 《Applied mathematics and computation》2010,216(9):2771-2284
The -expansion method can be used for constructing exact travelling wave solutions of real nonlinear evolution equations. In this paper, we improve the -expansion method and explore new application of this method to (2+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation. New types of exact complex travelling wave solutions of (2+1)-dimensional BKP equation are found. Some exact solutions of (2+1)-dimensional BKP equation obtained before are special cases of our results in this paper. 相似文献
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利用推广的(G′/G)展开法,研究了Zhiber-Shabat方程的行波解,获得了其各种孤子解和周期波解,并且给出了由它得来的著名方程Liouville方程的精确解,丰富了解的范围. 相似文献
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把最近提出的G′/G展开法推广到了非线性微分差分方程,利用该方法成功构造了一种修正的Volterra链和Toda链的双曲函数、三角函数以及有理函数三类涉及任意参数的行波解,当这些参数取特殊值时,可得这两个方程的扭状孤立波解、奇异行波解以及三角函数状的周期波解等.研究结果表明,该算法探讨非线性微分差分方程精确解十分有效、简洁. 相似文献
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利用(G'/G)法求解了Dodd-Bullough-Mikhailov的精确解,得到了Dodd-Bullough-Mikhailov方程的用双曲函数,三角函数和有理函数表示的三类精确行波解.由于方法中的G为某个二阶常系数线性ODE的通解,故方法具有直接、简洁的优点;更重要的是,方法可用于求得其它许多非线性演化方程的行波解.如果对其中双曲函数表示的行波解中的参数取特殊值,那么可得已有的孤波解. 相似文献
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Zhouzheng Kang 《偏微分方程(英文版)》2015,28(2):158-166
In this paper,with the aid of symbolic computation, themodified Benjamin- Bona-Mahony and Ostrovsky-Benjamin-Bona-Mahony equations are investigated by extended (G'/G2)-expansion method. As a consequence, some trigonometric, hyperbolic and rational function solutions with multiple arbitrary parameters for the two equations are revealed, which helps to illustrate the effectiveness of this method. 相似文献
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An analytic study of the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation is presented in this paper. The Riccati equation method combined with the generalized extended $(G''/G)$-expansion method is an interesting approach to find more general exact solutions of the nonlinear evolution equations in mathematical physics. We obtain the traveling wave solutions involving parameters, which are expressed by the hyperbolic and trigonometric function solutions. When the parameters are taken as special values, the solitary and periodic wave solutions are given. Comparison of our new results in this paper with the well-known results are given. 相似文献
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Kamruzzaman Khan Md. Abdus Salam Manik Mondal M. Ali Akbar 《Mathematical Methods in the Applied Sciences》2023,46(2):2042-2054
Traveling wave solutions have played a vital role in demonstrating the wave character of nonlinear problems emerging in the field of mathematical sciences and engineering. To depict the nature of propagation of the nonlinear waves in nature, a range of nonlinear evolution equations has been proposed and investigated in the existing literature. In this article, solitary and traveling periodic wave solutions for the (2 + 1)-dimensional modified KdV-KP equation are derived by employing an ansatz method, named the enhanced (G′/G)-expansion method. For this continued equation, abundant solitary wave solutions and nonlinear periodic wave solutions, along with some free parameters, are obtained. We have derived the exact expressions for the solitary waves that arise in the continuum-modified KdV-KP model. We study the significance of parameters numerically that arise in the obtained solutions. These parameters play an important role in the physical structure and propagation directions of the wave that characterizes the wave pattern. We discuss the relation between velocity and parameters and illustrate them graphically. Our numerical analysis suggests that the taller solitons are narrower than shorter waves and can travel faster. In addition, graphical representations of some obtained solutions along with their contour plot and wave train profiles are presented. The speed, as well as the profile of these solitary waves, is highly sensitive to the free parameters. Our results establish that the continuum-modified KdV-KP system supports solitary waves having different shapes and speeds for different values of the parameters. 相似文献
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结合齐次平衡法原理并利用(G'/G)-展开法,研究了广义的(2+1)维ZK-MEW方程的精确解,从而得到了广义的(2+1)维ZK-MEW方程的用双曲函数和三角函数表示的通解,当双曲函数通解中常数取特殊值时,便得到广义的(2+1)维ZK-MEW方程的孤立波解,获得了与现有文献不同的新精确解. 相似文献
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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