A Remark on the Commuting Flows Defined by Lax Equations

The Lax forms of many soliton-like equations such as the Burgers equation, the Dym equation, etc. are given. Relaxing the conditions imposed on the formal pseudo-differential operator in Sato theory of the KP-hierarchy, we obtain hierarchies of soliton-like equations. The Burgers hierarchy or the Dym hierarchy is obtained by a reduction of the original hierarchy of differential equations. We can also obtain many other hierarchies of soliton-like equations.