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1.
Mustafa Inc 《Central European Journal of Physics》2007,5(3):351-366
In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the sine-cosine method. As a result,
compactons, periodic, and singular periodic wave solutions are found.
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2.
In the present paper, the two-dimensional quantum Zakharov-Kuznetsov (QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations. 相似文献
3.
Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients are studied using the solutions
of Raccati equation. The solitary wave-like solution, the trigonometric periodic wave solution and the rational wave solution
are obtained with a constraint between coefficients. The property of the solutions is numerically investigated. It is shown
that the coefficients of the equation do not change the wave amplitude, but may change the wave velocity.
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4.
In the present paper, the two-dimensional quantum Zakharov-Kuznetsov(QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations. 相似文献
5.
In this paper, we find exact solutions of some nonlinear evolution equations by using generalized tanh–coth method. Three nonlinear models of physical significance, i.e. the Cahn–Hilliard equation, the Allen–Cahn equation and the steady-state equation with a cubic nonlinearity are considered and their exact solutions are obtained. From the general solutions, other well-known results are also derived. Also in this paper, we shall compare the generalized tanh–coth method and generalized (G ′/G )-expansion method to solve partial differential equations (PDEs) and ordinary differential equations (ODEs). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important roles in engineering fields. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized tanh–coth method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems. 相似文献
6.
The (G′/G)-expansion method and its simplified version are used to obtain generalized travelling wave solutions of five nonlinear evolution
equations (NLEEs) of physical importance, viz. the (2+1)-dimensional Maccari system, the Pochhammer–Chree equation, the Newell–Whitehead
equation, the Fitzhugh–Nagumo equation and the Burger–Fisher equation. A variety of special solutions like periodic, kink–antikink
solitons, bell-type solitons etc. can easily be derived from the general results. Three-dimensional profile plots of some
of the solutions are also drawn. 相似文献
7.
This paper obtains solitons and singular periodic solutions to the generalized resonant dispersive nonlinear Schrödinger’ equation with power law nonlinearity. There are several integration tools that are adopted to extract these solutions. They are simplest equation method, functional variable method, sine–cosine function method, tanh function method and the G′/G-expansion method. These integration techniques reveal bright and singular solitons as well as the corresponding singular periodic solutions to the nonlinear evolution equation. These solitons solutions are important in the nonlinear fiber optics community as well as in the study of rogue waves. 相似文献
8.
Abundant new exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered. 相似文献
9.
In this paper, an extended multiple (G′/G)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the
proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the
generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation
and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric
functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values,
the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this
method can also be used to deal with some high-dimensional and variable coefficients’ nonlinear evolution equations. 相似文献
10.
S. M. Rayhanul Islam Kamruzzaman Khan K. M. Abdul Al Woadud 《Waves in Random and Complex Media》2018,28(2):300-309
The enhanced (G′/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney–Luke equation by using the enhanced (G′/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper. 相似文献
11.
Mohammed K. Elboree 《理论物理通讯》2015,64(4):379-390
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics. 相似文献
12.
《Waves in Random and Complex Media》2013,23(2):378-385
This paper obtains the soliton solutions of the Gilson–Pickering equation. The G′/G method will be used to carry out the solutions of this equation and then the solitary wave ansatz method will be used to obtain a 1-soliton solution of this equation. Finally, the invariance and multiplier approach will be applied to recover a few of the conserved quantities of this equation. 相似文献
13.
Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity are obtained using the mapping method. Several
solutions are determined inclusing the cnoidal waves, shock waves, solitary waves, periodic singular waves and others. Finally,
the ansatz method is applied to solve the equation with power law nonlinearity. It has been proved that the shock waves or
topological solitons exist only for specific values of the power law parameter. 相似文献
14.
In this article, the novel (G ′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed. 相似文献
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16.
In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G??/G)-expansion method, where G?=?G(??) satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained. 相似文献
17.
利用改进的直接方法给出了一类广义Zakharov-Kuznetsov方程ut auux bu2ux cuxxx duxyy=0新显式解与旧显式解之间的关系,并且得到了该方程的对称.这些对称推广了已有文献中应用Steinberg s相似方法获得的结果.利用广义Zakharov-Kuznetsov方程新旧显式解之间的关系,本文在已有显式解的基础上给出了方程新的显式解.这些解对于研究某些复杂的物理现象,以及验证数值求解法则的可行性有重要的意义. 相似文献
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19.
利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明,同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展, 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.
关键词:
同伦分析法
改进的 Zakharov-Kuznetsov方程
周期解 相似文献
20.
This paper studies the Klein?CGordon?CZakharov equation with power-law nonlinearity. This is a coupled nonlinear evolution equation. The solutions for this equation are obtained by the travelling wave hypothesis method, (G??/G) method and the mapping method. 相似文献