KdV方程的一种新解法

Solution for KdV Equation

提出一种求解KdV方程的新方法,即利用齐次平衡原则及F展开法的思想求出其丰富的精确解,包括椭圆函数、双曲函数和三角函数表示的精确解,其中包含正负幂项的解是新形式的精确解。此方法为求解类似方程提供了借鉴。

A new method of solving nonlinear KdV equation is introduced. By using the homogeneous balance principle (HBP) and the F-expansion method proposed recently, abundant exact solutions expressed by ellipticfunction, hyperbolic function, and trigonometric function for KdV equation are obtained, and the exact solutions whichinclude positive and negative power items are new. The method can be applied to solve more nonlinear partialdifferential equations.