1) KdV system
KdV系统
1.
In this paper, we extend this method to a generalized KdV system, abundant traveling wave solutions of this system, such as solitary wave solutions, periodic wave solutions and others rational function solutions, ar.
将上述方法进一步推广到广义的KdV系统,获得了该系统丰富的精确行波解,包括孤波解、周期波解和奇异解。
2) variable coefficient KdV equation
变系数KdV方程
1.
Exact solutions of the general variable coefficient KdV equation with external force term;
含外力项的广义变系数KdV方程的精确解
2.
By using a transformation,the variable coefficient KdV equation is reduced to a nonlinear ordinary differential equation(NLODE).
利用一种函数变换将变系数KdV方程约化为非线性常微分方程(NLODE),并由此NLODE出发获得变系数KdV方程的若干精确类孤子解。
3.
In this paper,by using of new special function transform in truncated expansion method,the three kinds of exact solutions of the general variable coefficient KdV equation are obtained.
文章在截断展开法中采用特殊的函数变换形式,从而求出了广义变系数KdV方程三类新的精确解。
3) KdV equation with variable coefficients
变系数KdV方程
1.
New exact solutions of the (2+1)-dimensional KdV equation with variable coefficients;
(2+1)维变系数KdV方程的新精确解
2.
Solving KdV equation with variable coefficients by using F-expansion method;
用F展开法解变系数KdV方程
3.
Exact solutions,solitary wave solution and travelling wave solutions are given for the KdV equation with variable coefficients.
通过齐次平衡法及可化为Bernoulli方程的四阶常微分方程,求出了变系数KdV方程的精确解及孤立波解。
4) KdV equations with variable coefficients
变系数KdV方程组
1.
In this paper,by using the homogenous balance principle and F-expansion method,the periodic wave solutions expressed by Jacobi elliptic fuctions to the KdV equations with variable coefficients are derived,and in the limit case,the solitary wave solutions and other type solutions for KdV equations with variable coefficients equations are obtained as well.
利用F-展开法和齐次平衡原则,求出了变系数KdV方程组的Jacobi椭圆函数表示的周期解,在极限情况下,得到变系数KdV方程组的孤波解以及其它形式的解。
5) (n,m) th KdV hierarchy
(n,m)阶KdV系列
6) variable coefficients KdV-Burgers equation
变系数KdV-Burgers方程
1.
With the Painlevé test method and computer symbolic computation,the paper studies the generalized variable coefficients KdV-Burgers equation to obtain the integral conditions of that equation and the binding conditions between the variable coefficients.
利用Painlevé分析方法,借助计算机符号运算,研究了广义变系数KdV-Burgers方程,得出该方程的可积条件,从而获得变系数间的约束条件。
补充资料：Kdv方程
Image:11776596881617173.jpg
kdv方程
kdv方程是1895年由荷兰数学家科特韦格和德弗里斯共同发现的一种偏微分方程（也有人称之为科特韦格-德弗里斯方程，但一般都习惯直接叫kdv方程）。
kdv方程的解为簇集的孤立子（又称孤子，孤波）。
kdv方程和物理问题有几个联系。 它是弦在fermi-pasta-ulam问题在连续极限下的统治方程。kdv方程也描述弱非线性回复力的浅水波。
kdv方程也可以用逆散射技术求解，譬如那些适用于薛定谔方程的。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。