一维和二维KdV方程的有理函数解

The Rational Solution of One and Two Dimensional KdV Equation

求解非线性偏微分方程的方法很多 ,不同的方法用于不同的方程其有效性也各不相同 .齐次平衡法是把非线性偏微分方程转换成约束条件的线性偏微分方程的一种很好的方法 .利用齐次平衡法具体讨论了KdV方程和二维KdV方程更具一般形式的有理函数解 .

In general, there are many methods to resolve the PDE and their validity is difference. In this paper, based on homogeneous balance method,we introduced an improved method:changing the original nonlinear PDE into the linear PDE with some constraint conditions. Using this method, we achieved the general rational solutions of KdV and KP.