类9阶KdV方程的有理解

Rational solutions to ninth-order KdV-like equations

对于9阶KdV方程,利用广义双线性算子定义,并基于素数p=2,3,5,7,将它转化成4个不同的类9阶KdV方程。通过符号计算,基于贝尔多项式理论,得到了4个广义双线性微分方程关于空间变量x的10次以内全部多项式解,进而求出了4个类9阶KdV方程的21类有理解。

For the ninth-order KdV equation,based on the prime numbers p=2,3,5,7,four extended ninth-order KdV-like equations are derived from it by the generalized bilinear differential operators.By means of symbolic computation,based on Bell polynomial theory,all polynomial solutions to the four generalized bilinear differential equations within the tenth order of the space variable x are obtained,and then 21 types of rational solutions to the four ninth-order KdV-like equations are obtained through the polynomial solutions.