一般变系数耗散长水波方程的精确解

By using the homogeneous balance principle(HBP),we derive a B■cklund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.     

Whitham-Broer-Kaup浅水波方程的Backlund变换和精确解

用一种新的方法并借助Mathematica,求出了Whitham-Broer-Kaup(简记WBK)方程的一种Backlund变换,并建立了WBK方程与热传导方程及Burgers方程的联系.利用这种关系得到了WBK方程的三组精确解,其中一组为孤波解.     

推广的F -展开法及变系数KdV和mKdV的精确解

该文首先推广了新近提出的F -展开法,利用该方法导出了变系数KdV和mKdV方程 的类椭圆函数解;并在极限的情况下,得到变系数KdV和 mKdV方程变波速和变波长的类孤子解以及其他形式解.     

一变系数非线性发展方程组的自-BT及其精确解

利用齐次平衡原则,导出了一变系数非线性发展方程组的自-Baecklund变换(自-BT);借助此自-BT和变系数热传导方程的各种精确解用代数的方法获得了方程组的各种精确解。     

齐次平衡法和浅水波中WBK方程的精确分析解

Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan‘s, Xie‘s and Yan‘s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.     

Exact solitary wave solutions to a combined KdV and mKdV equation

An exact travelling wave kink soliton to a combination KdV and mKdV equations is given by using an effective homogeneous balance method, and a two‐dimensional generalization is also discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

一类非线性方程的Backlund变换以及紧孤立波解的线性稳定性

引进五阶线性色散项方程K(m,n,1),用逆算符方法得到了sin型多重compacton 解(紧孤立波解);利用齐次平衡法得到了K(2,2,1)方程的Backlund变换,并且得到一些新的孤立波解;最后研究了sin型多重compacton解的线性稳定性.     

变系数二阶线性微分方程的一个新的可解类型

通过双变换——未知函数的线性变换和自变量变换 ,将一类变系数线性微分方程化为二阶常系数线性微分方程 ,从而得到变系数二阶线性微分方程的一个新的可解类型 ,推广了著名的二阶 Euler方程 .     

复杂边界条件下任意变系数微分方程的半解析方法

利用有限元和矩阵函数的有关理论与变系数等效参数相结合,提出了一种求解变系数微分方程的解法,利用它能方便地处理由于各种原因导致其控制方程是变系数的微分方程,最后通过两个算例,取得了满意的结果.     

Bcklund transformation, non-local symmetry and exact solutions for (2+1)-dimensional variable coefficient generalized KP equations

IntroductionDuring the study of water wave, many completely iategrable models were derived, such as(1+1)-dimensional KdV equation, MKdV equation, (2+1)-dimensional KdV equation, Boussinesq equation and WBK equations etc. Many properties of these models had been researched,such as BAcklund transformation (BT), converse rules, N-soliton solutions and Painleve property etc.II--8]. In this paper, we would like to consider (2+1)-dimensional variable coefficientgeneralized KP equation which …     

Asymptotic behavior of the periodic wave solution for the (3+1)-dimensional Kadomtsev-Petviashvili equation

In this paper, the one- and two-periodic wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are presented by means of the Hirota’s bilinear method and the Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.     

Exact solutions of nonlinear evolution equations with variable coefficients using exp-function method

In this paper, we apply the exp-function method to construct generalized solitary and periodic solutions of nonlinear evolution equations with variable coefficients. The proposed technique is tested on the Zakharov-Kuznetsov and (2+1)-dimensional Broer-Kaup equations with variable coefficients. These equations play a very important role in mathematical physics and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. Obtained results clearly indicate the reliability and efficiency of the proposed exp-function method.     

Brusselator反应扩展模型的Auto—Darboux变换和精确解

首先用改进的齐次平衡法,获得了Brusselator反应扩散模型的Auto-Darboux变换（ADT）,基于这个ADT,若干精确解被得到,其中包括一些作者的已知结果,然后,通过用一系列变换,这个模型约化为一个非线性反应扩展方程,再采用sine-consine方法,获得了更多的精确解,其中包括新的孤子解。     

New soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation

The repeated homogeneous balance is used to construct a new exact traveling wave solution of the Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can be applied to other nonlinear evolution equations.     

含外力项的广义KdV方程的新自Darboux变换和显式解析解

基于 Ｒｉｃｃａｔｉ形式的 Ｌａｘ对,本文推得了含外力项的广义 ＫｄＶ方程的新自Ｄａｒｂｏｕｘ变换．当应用这个变换时,仅需要做积分,就能获得一系列显示解析解,其中包含类孤波解．这种途径对于寻找非线性发展方程新的具有物理意义的解或许是有用的．     

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.     

(2+1)维浅水波方程的新精确解

对(2+1)维浅水波方程的现有解进行了推广.应用CK方法对方程进行求解,得到方程的Backlund变换公式,将已知解代入公式,求得一些新的精确解,从而推广了浅水渡方程的解.     

扩展的(G'/G)展开法求量子Zakharov-Kuznetsov方程的精确解

为得到量子Zakharov-Kuznetsov方程的一些新精确解,借助行波解的思想,结合齐次平衡原理和一类非线性常微分方程解的结构,利用扩展的(G'/G)展开方法,研究了其相应的更加丰富的精确解表达形式.新精确解的表达式主要由双曲函数、三角函数和有理数函数构成,出现了某些怪波解的情形.通过对比不同情况下解的形式,利用M...     

非线性系统的精确解

Based on the computerized symbolic, a new generalized tanh functions method is used for constructing exact travelling wave solutions of nonlinear partial differential equations （PDES） in a unified way. The main idea of our method is to take full advantage of an auxiliary ordinary differential equation which has more new solutions. At the same time, we present a more general transformation, which is a generalized method for finding more types of travelling wave solutions of nonlinear evolution equations （NLEEs）. More new exact travelling wave solutions to two nonlinear systems are explicitly obtained.     

(3+1)维变系数Kudryashov-Sinelshchikov(K-S)方程的同宿呼吸波解和高阶怪波解

基于Hirota双线性方法,利用拓展的同宿呼吸检验法得到了(3+1)维变系数Kudryashov-Sinelshchikov(K-S)方程的同宿呼吸波解,对该解的参数选取合适的数值,可得到不同结构的同宿呼吸波.通过对同宿呼吸波解的周期取极限,推导出方程的怪波解.最后,构造出一个特殊的高阶多项式作为测试函数,求得该方程的一阶怪波解和二阶怪波解.