Abstract: Based on conservative equation of potential vorticity,it is proved that the atmospheric nonlinear evolution in weak frequency-dispersion condition is usually governed by KdV equation and the forms of weak frequency-dispersion conditionsare discussed.Sonm prvious researches on derivation of KdV equation from different specified atmospheric motions are actually the special cases of the general form in this paper.The KdV equation can be resolved by numerical method.The resulte present that the initial disturbance in limited domain will develop the isolated wave under one given condition and a series of frequency-dispersing waves under other given conditions.