广义KdV孤子解和广义KdV-Burgers行波解的条件稳定性

对于一类KdV方程的孤子解和一类KdV-Burgers方程的行波解，利用直接扰动法证明了它们具有条件稳定性，即解的稳定性敏感的依赖于方程的参数和初始条件，从而推广和修正了近期文献中关于这些解不稳定的结论. 关键词：     

KdV型方程孤波解与KdV-Burgers型方程行波解的稳定性

证明了KdV型议程的孤波解和KdV-Burgers型方程的行波解在李亚诺夫意义下是不是稳定的，从而修正了文献中的一些结论。     

KdV-Burgers方程的孤波解

对双曲函数法进行了深入探讨,推广了该方法的某些使用条件,借助计算机代数系统Mathe matica,进一步获得了KdV-Burgers方程的两组扭状孤波解. 关键词： 双曲函数法 KdV-Burgers方程 行波解 计算机代数系统Mathe matica     

扰动Vakhnenko方程物理模型的行波解

研究了一类扰动Vakhnemko方程.给出了改进的渐近方法.首先, 对原模型系统对应的典型方程得到对应的行波解.其次, 引入一个泛函, 建立迭代关系式,将求解非线性问题转化为求解一系列的迭代序列.然后, 逐次地求出对应的解的近似式, 最后,得到了原扰动Vakhnemko模型行波解的任意次精度的近似展开式,并讨论了它的精度. 关键词： 泛函 行波解 Vakhnemko方程     

KdVB方程行波解的渐近分析

本文利用奇异摄动的理论和方法,研究v²?4μ时KdVB方程的行波解,得到行波解的三阶渐近展开式的显式,同时得到行波解的一般渐近展开式的表达式:u≈u⁽⁰⁾+εu⁽¹⁾+ε¹u⁽²⁾+…+εⁿu⁽ⁿ⁾+…;并且证明u^(j)(j=1,2,…,n,…)都是有界函数。 关键词：     

若干非线性波方程的行波解

在求一类非线性波方程行波解时,先将有关的非线性常微分方程在其Poincaré相平面上作定性分析,然后再区别情况求积分,从而得到了各式各样的行波解。 关键词：     

一类广义扰动KdV-Burgers方程的同伦近似解

通过构造一个同伦映射, 研究了一类广义扰动KdV-Burgers方程. 在引入典型无扰动任意次广义KdV-Burgers方程扭状孤立波解的基础上, 研究了扰动方程的具有任意精度的近似解,指出了近似解级数的收敛性, 最后利用不动点定理,进一步说明近似解的有效性,并对精度进行了讨论. 关键词： 广义扰动KdV-Burgers方程 同伦映射 渐近方法 近似解     

KdV方程与高阶KdV方程行波解之间的形变理论

从具有较多参数的复杂非线性方程的解出发,取某些参数的极限,这些解就退化到具有较少参数的简单方程的解,本文以KdV方程的行波解为例说明对于某些特解,上述极限过程的逆过程,即将简单方程的解形变到复杂方程的解是可能的,但一般来说并不一定具有唯一性。 关键词：     

一类非线性演化方程新的显式行波解

借助Mathematica软件,采用三角函数法和吴文俊消元法,获得了一类非线性演化方程u_tt+au_xx+bu+cu³=0的三组行波解,其中包括新的行波解、扭状孤波解和钟状孤波解.从而作为该方程的特例,如Duffing方,Klein-Gordon方程、Landau-Ginburg-Higgs方程和⁴方程等也都获得了相应的若干行波解.这种方法也适用于其他非线性方程. 关键词：     

Some New Solitary Wave Solutions to a Compound KdV-Burgers Equation

Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f （ξ）, is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations.     

Some New Solitary Wave Solutions to a Compound KdV-Burgers Equation

In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f(ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations.     

New Solitary Wave Solutions to the KdV-Burgers Equation

Based on the analysis on the features of the Burgers equation and KdV equation as well as KdV-Burgers equation, a superposition method is proposed to construct the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and KdV equation, and then by using it we obtain many solitary wave solutions to the KdV-Burgers equation, some of which are new ones.PACS: 02.30.Jr; 03.65.Ge     

New Travelling Wave Solutions to Compound KdV-Burgers Equation

The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics. In this paper, applying the improved trigonometric function method to these equations, rich explicit and exact travelling wave solutions, which contain solitary-wave solutions, periodic solutions, and combined formal solitary-wave solutions, are obtained.     

Representations and Classification of Traveling Wave Solutions to sinh-GSrdon Equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. （Beijing, China） 45 （2006） 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.     

Some New Exact Traveling Wave Solutions of Double-sine-Gordon Equation

The double-sine-Gordon equation is studied by means of the so-called mapping method. Some new exact solutions are determined.     

Traveling Wave Solutions for Generalized Bretherton Equation

This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He's semi-inverse method (He's variational method). Various traveling wave solutions are obtained, revealing anintrinsic relationship among the amplitude, frequency, and wave speed.     

Bifurcations and Dynamics of Traveling Wave Solutions to a Fujimoto-Watanabe Equation

In this paper, we study the bifurcations and dynamics of traveling wave solutions to a Fujimoto-Watanabe equation by using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the parametric space. Then we show the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, compactions and kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions and periodic wave solutions are implicitly given,while the expressions of kink-like and antikink-like wave solutions are explicitly shown. The dynamics of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of the nonlinear wave.     

Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.     

Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travellingwave form satisfies some special conditions.