应用辅助方程法求Zakharov方程的精确解

应用辅助方程法求得Zakharov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,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明:辅助方程法在非线性光学、量子光学、激光物理和等离子体物理等领域具有广泛的应用.     

应用G/G′展开法求Ostrovsky方程的孤子解

应用(G/G')展开法构造出(1+1)维0strovsky方程的10组精确解,这些解的类型主要包含双曲函数通解、三角函数通解和有理函数通解三种形式.对解的性质进行了相应地分析,当对双曲函数通解中的参数取特殊值时,可以得到了孤立波解.当对三角函数通解中引中的参数取特殊值时,可以得到对应的周期波函数解.     

几个非线性发展方程的精确解

应用改进F/G展开法求得(2+1)维BBM方程、(1+1)维Benjiamin Ono方程、广义(2+1)维ZK-MEW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,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明,F/G展开法在非线性发展方程中具有广泛的应用.     

利用改进的(G/G)-展开法求广义的(21)维 Boussinesq 方程的精确解

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.     

利用改进的(G′/G)-展开法求广义的(2+1)维Boussinesq方程的精确解

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.     

Dodd-Bullough-Mikhailov方程的精确解

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.     

变系数李方程组的精确行波解

利用修正的简单方程法对变系数李方程组进行求解,给出了变系数李方程组的双曲函数形式的行波解,当参数取特殊值时,便可以得到该方程组的精确孤波解.     

构造非线性微分差分方程精确解的一种方法

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.     

(2+1)维Broer-Kaup-Kupershmidt方程组的行波解

借助于计算机代数系统Mathematica,利用推广的简单方程方法构造了(2+1)维Broer-Kaup-Kupershmidt方程组的新的精确行波解,分别以含有双参数的用双曲函数,三角函数和有理函数表示,其中双曲函数表.示的行波解中参数取特殊值时可得到文献已有的孤波解.方法也适用于其它非线性发展方程(组).     

利用(G'/G)-展开法求广义的(2+1)维ZK-MEW方程的新精确解

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.     

The extended Riccati equation method for travelling wave solutions of ZK equation

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.     

The Exact Solutions for the Benjamin-Bona-Mahony Equation

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.     

The Riccati Equation Method Combined with the Generalized Extended $(G'/G)$-Expansion Method for Solving the Nonlinear KPP Equation

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.     

应用(1/G)-展开法求解五阶KdV方程

本篇论文首次提出(1/G) -展开法,用于求解非线性演化方程的行波解.将该法应用于五阶KdV方程的求解,当参数满足一定条件时,该方程可化为Sawada-Kotera (SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt (KK)方程、Lax方程和Ito方程.其解可被表示为...     

Application of the improved F-expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations

In this article, we pay attention to the analytical method named, the improved F-expansion method combined with Riccati equation for finding the exact traveling wave solutions of the Benney–Luke equation and the Phi-4 equation. By means of this method we have explored three classes of explicit solutions-hyperbolic, trigonometric and rational solutions with some free parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. Our outcomes disclose that this method is very active and forthright way of formulating the exact solutions of nonlinear evolution equations arising in mathematical physics and engineering.     

利用推广的(G′/G)展开法求解(2+1)维BBM方程

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.     

一类推广的KdV方程的新行波解

本文研究了一类推广的Kd V方程的行波解求解的问题.利用新的G展开法,并借助Mathematica计算软件,获得了该方程的含有多个任意参数的新的行波解,分别为三角函数解、双曲函数解、有理函数解和指数函数解,扩大了该类方程的解的范围.