An equation to describe a weakly unstable region of a uniformly fluidi
zed bed in both gas solid mixtures and liquid-solid mixtures is derive
d from a two-fluid model by applying the reductive perturbation method
. Our reduced equation near the transition point from stable fluidized
beds to unstable ones is the Korteweg-de Vries equation. When the sta
te is away from the critical point the effects of dissipations become
important. The validity of our reduced equation has been confirmed by
our numerical simulation.