Hi all. I am referring to the Kdv equtaion as follows: u_t = u u_x + u_(xxx) A fundamental point concerning the KdV equation is that it exhibits two opposing tendencies: 1. "nonlinear convection", uu_x, which tends to -steepen- wavecrests, 2. "dispersion", u_(xxx), which tends to -flatten- wave crests. However, I don't quite understand why the nonlinear term and the disperion term would tend to steepen the wave profile? Could I see this through the geometrical meaning of uu_x and u_(xxx) or what? how could one make such a statment?