变系数广义KdV方程新的类孤波解和精确解

用普通KdV方程作变换,构造变系数广义KdV方程的解,获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词：KdV方程变系数广义KdV方程类孤波解精确解     

广义随机KdV方程新的精确类孤子解

利用厄米(Hermite)变换求出了广义随机KdV方程新的类孤子解.这种方法的基本思想是通过厄米变换把Wick类型的广义随机KdV变成广义变系数KdV方程,利用特殊的截断展开方法求出 方程的解,然后通过厄米的逆变换求出方程的随机解.关键词：随机KdV方程随机孤子解白色噪音截断展开方法厄米变换     

截断展开方法和广义变系数KdV方程新的精确类孤子解

利用特殊的截断展开方法求出了广义变系数KdV方程新的类孤子解.这种方法的基本思想是假定形式解具有截断展开形式,以致可把广义变系数KdV方程转化为一组待定函数的代数方程组,进而给出待定函数容易积分的常微分方程.利用例子证明了这种方法是十分有效的.关键词：截断展开法变系数KdV方程孤波解     

含外力项的广义KdV方程的类孤子解

本文利用广义KP方程的B?cklund变换,获得了含外力项的广义KdV方程u_t+6uu_x+u_xxx+6f(t)u=g(t)+x(f′+12f²) (1)的类孤子解。关键词：     

具有三个任意函数的变系数KdV-MKdV方程的精确类孤子解

利用一个新的变换将变系数KdV-MKdV方程约化为三阶非线性常微分方程(NODE),考虑这个NODE,获得了变系数KdV-MKdV方程的若干精确类孤子解.这种思路也适合于其他的变系数非线性方程,如变系数KP方程、变系数sine-Gordon方程等.关键词：     

(3+1)维 KdV 方程新的精确解和孤子解

用普通Korteweg-de Vries(KdV)方程作变换,构造(3 1)维KdV方程的解,获得了新的孤子解、Jaoobi椭圆函数解、三角函数解和Weierstrass椭圆函数解.     

MKdV方程的拟小波解

用拟小波方法求MKdV方程的数值解-先用拟小波离散格式离散空间导数,然后用四阶Runge-Kutta方法离散时间导数,对一个有精确解的实例ut+6u2ux+uxxx=0进行了数值计算-拟小波解与解析解完全重合,t=10000s时,二者也没有偏差-关键词：MKdV方程拟小波方法孤子解     

一类广义Boussinesq方程和Boussinesq-Burgers方程新的显式精确解

利用一种推广的代数方法,求解了一类广义Boussinesq方程(B(m,n)方程)和Boussinesq-Burgers方程(B-B方程).获得了其多种形式的显式精确解,包括孤波解、三角函数解、有理函数解、Jacobi椭圆函数周期解和Weierstrass椭圆函数周期解,进一步丰富了这两类方程的解.关键词：Boussinesq方程Boussinesq-Burgers方程推广的代数方法显式精确解     

广义五阶KdV方程的孤波解与孤子解

利用求解非线性代数方程组的吴文俊特征列方法,借助计算机代数系统获得了一类较广泛的五阶非线性演化方程的孤波解和孤子解,修正和完善了已知的结论关键词：五阶KdV方程孤波孤子解     

用试探方程法求变系数非线性发展方程的精确解

将试探方程法应用到变系数非线性发展方程的精确解的求解.以两类变系数KdV方程为例,在相当一般的参数条件下求得了丰富的精确解,其中包括新解.关键词：试探方程法变系数KdV方程类椭圆正弦(余弦)波解类孤子解     

A New Modified Extended Tanh-Function Method and Its Application

In this paper, a new modified extended tanh-function method is presented for constructing soliton-like,periodic form solutions of nonlinear evolution equation (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A277 (2000) 212] and the moditied extended tanh-function method [Phys. Lett. A285(2001) 355]. Abundant new solutions of two physically important NEEs are obtained by using this method and symbolic computation system Maple.     

New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii‘s generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.     

New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Left. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Left. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii‘s generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.     

On a New Modified Extended Tanh-Function Method

In this paper, a new modified extended tanh-function method is presented for constructing multiple soliton-like, periodic form and rational solutions of nonlinear evolution equations (NLEEs). This method is more powerful thanthe extended tanh-function method [Phys. Lett. A277 (2000) 212] and the modified extended tanh-function method[Phys. Lett. A299 (2002) 179] Abundant new solutions of two physically important NLEEs are obtained by using thismethod and symbolic computation system Maple.     

New Exact Solutions of the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces

In this paper, by improving some procedure ofextended tanh-function method, some new exact solutions to theintegrable Broer-Kaup equations in (2+1)-dimensional spacesare obtained, which include soliton-like solutions, solitary wave solutions,trigonometric function solutions, and rational solutions.     

Explicit Exact Solutions for the (2+1)-Dimensional Higher-Order Broer-Kaup System

Using the modified extended tanh-function method, explicit and exact traveling wave solutions for the (2+1)-dimensional higher-order Broer-Kaup (HBK) system, comprising new soliton-like and period-form solutions, are obtained.     

The soliton-like solutions to the （2＋1）-dimensional modified dispersive water-wave system

By a simple transformation, we reduce the (2 1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method.     

New Families of Exact Solutions for (2+1)-Dimensional Broer-Kaup System

Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.     

Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to(1+1)-Dimensional Dispersive Long Wave Equation

In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.