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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?