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1.
Abundant explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law nonlinearities 下载免费PDF全文
This paper is concerned with the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law. Abundant explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
2.
Li-Ying YangGuan-Ting Liu 《Applied mathematics and computation》2011,217(18):7377-7384
Using the differential transformation method and the homogeneous balance method, some new solutions of an auxiliary elliptic equation are obtained. These solutions possess the forms of rational functions in terms of trigonometric functions, hyperbolic functions, exponential functions, power functions, elliptic functions and their operation and composite functions and so on, which are so-called quasi-rational function solutions. Based on these new quasi-rational functions solutions, a direct method is proposed to construct the exact solutions of some nonlinear evolution equations with the aid of symbolic computation. The coupled KdV-mKdV equation and Broer-Kaup equations are chosen to illustrate the effectiveness and convenience of the suggested method for obtaining quasi-rational function solutions of nonlinear evolution equations. 相似文献
3.
In this paper, we focus on the interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation. With symbolic computation, two types of interaction solutions including lump-kink and lump-soliton ones are derived through mixing two positive quadratic functions with an exponential function, or two positive quadratic functions with a hyperbolic cosine function in the bilinear equation. The completely non-elastic interaction between a lump and a stripe is presented, which shows the lump is drowned or shallowed by the stripe. The interaction between lump and soliton is also given, where the lump moves from one branch to the other branch of the soliton. These phenomena exhibit the dynamics of nonlinear waves and the solutions are useful for the study on interaction behavior of nonlinear waves in shallow water, plasma, nonlinear optics and Bose–Einstein condensates. 相似文献
4.
In this article, the extended Riccati equation method is applied to seeking more general exact travelling wave solutions of the ZK equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. When the parameters are taken as special values, the solitary wave solutions are obtained from the hyperbolic function solutions. Similarly, the periodic wave solutions are also obtained from the trigonometric function solutions. The approach developed in this paper is effective and it may also be used for solving many other nonlinear evolution equations in mathematical physics. 相似文献
5.
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
6.
Luis Verde-Star 《Journal of Mathematical Analysis and Applications》2002,274(2):755-771
The authors aim here at finding all the generalizations of the binomial formula that are given by a generating-function of the generalized Appell form for a sequence of Newton polynomials. The formulas obtained include the well-known q-analogue of the binomial formula, several formulas involving hyperbolic functions, a trigonometric analogue, and some formulas involving the geometric and the exponential series. 相似文献
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In the present work, we dealt with exact solutions and conservation laws of the Benjamin-Ono equation. We obtained exact solutions of given equation via the exp$(-\Phi (\xi ))$ method. The obtained solutions are included the hyperbolic functions, trigonometric functions and rational functions. By using the multiplier approach, the conservation laws of the mentioned equation was founded. 相似文献
9.
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
10.
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
11.
Lumps and their interaction solutions of a (2+1)-dimensional generalized potential Kadomtsev-Petviashvili equation 下载免费PDF全文
A (2+1)-dimensional generalized potential Kadomtsev-Petviashvili (gpKP) equation which possesses a Hirota bilinear form is constructed. The lump waves are derived by using a positive quadratic function solution. By combining an exponential function with a quadratic function, an interaction solution between a lump and a one-kink soliton is obtained. Furthermore, an interaction solution between a lump and a two-kink soliton is presented by mixing two exponential functions with a quadratic function. This type of lump wave just appears to a line $k_2x+k_3y+k_4t+k_5 \sim 0$. We call this kind of lump wave is a special rogue wave. Some visual figures are depicted to explain the propagation phenomena of these interaction solutions. 相似文献
12.
应用改进的简单方程法求得Cahn-Allen方程和Jimbo-Miwa方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可以得到了孤立波解.当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,简单方程法对于研究非线性数学物理方程具有非常广泛的应用意义. 相似文献
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利用一种改进的统一代数方法将构造(2+1)维ZK MEW((2+1)-dimensionalZakharov-Kuznetsovmodifiedequalwidth)方程精确行波解的问题转化为求解一组非线性的代数方程组.再借助于符号计算系统Mathematica求解所得到的非线性代数方程组,最终获得了方程的多种形式的精确行波解.其中包括有理解,三角函数解,双曲函数解,双周期Jacobi椭圆函数解,双周期Weierstrass椭圆形式解等.并给出了部分解的图形. 相似文献
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Xiaofang Duan Junliang Lu Yaping Ren Rui Ma 《Journal of Nonlinear Modeling and Analysis》2022,4(4):628-649
The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional
propagation of nonlinear dispersive long waves, which has a clear
physical background, and is a more suitable mathematical and
physical equation than the KdV equation. Therefore, the research
on the BBM equation is very important. In this article, we put
forward an effective algorithm, the modified hyperbolic function
expanding method, to build the solutions of the BBM equation. We, by
utilizing the modified hyperbolic function expanding method,
obtain the traveling wave solutions of the BBM equation.
When the parameters are taken as special values, the solitary
waves are also derived from the traveling waves. The traveling
wave solutions are expressed by the hyperbolic functions, the
trigonometric functions and the rational functions. The modified
hyperbolic function expanding method is direct, concise, elementary
and effective, and can be used for many other nonlinear partial
differential equations. 相似文献
17.
We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions. 相似文献
18.
Filiz Tascan Ahmet Bekir Murat Koparan 《Communications in Nonlinear Science & Numerical Simulation》2009,14(5):1810-1815
In this paper, we established travelling wave solutions for some (2 + 1)-dimensional nonlinear evolution equations. The first integral method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The first integral method presents a wider applicability for handling nonlinear wave equations. 相似文献
19.
Yu.A. Melnikov 《Journal of Mathematical Analysis and Applications》2008,344(1):521-534
An innovative technique is developed for obtaining infinite product representations for some elementary functions. The technique is based on the comparison of alternative expressions of Green's functions constructed by two different methods. Some standard boundary value problems are considered posed for two-dimensional Laplace equation on regions of a regular configuration. Classical closed analytic form of Green's functions for such problems are compared against those obtained by the method of images in the form of infinite products. This yields a number of new infinite product representations for trigonometric and hyperbolic functions. 相似文献
20.
《Journal of the Egyptian Mathematical Society》2014,22(3):402-406
In this paper, we demonstrate the effectiveness of the new generalized (G′/G)-expansion method by seeking more exact solutions via the mKdV equation and the Gardner equations. The method is direct, concise and simple to implement compared to other existing methods. The traveling wave solutions obtained by this method are expressed in terms of hyperbolic, trigonometric and rational functions. The method shows a wide application for handling nonlinear wave equations. Moreover, the method reduces the large amount of calculations. 相似文献