一类广义KdV方程的行波解

由于非线性引起的脉冲的挤压与由色散引起的扩展相互抵消,可以使行波保持一个永久的形状,从而导致非线性色散方程孤子解的产生,据此我们修改KdV方程的非线性项,并利用齐次平衡原则获得了这类广义KdV方程的孤子解。

For nonlinear dispersion equation,because of mutual offset of nonlinear impulsive caused by effect of nonlinearity and expanding caused by the effect of dispersion,a permanent wave shape can be maintained to form of the solution of soliton.Based on this fact,we modify the nonlinear term of KdV equation and use the homogeneous balance principle to obtain the soliton solution of this socalled generalized KdV equation.