Algebraic aspects of Brockett type equations

It is well known that soliton equations can be written in Lax form, where t he bracket of two linear differential (n-KdV) or pseudo-differential (KP) o perators appears. In this work, we introduce a new hierarchy; each equation of which is defined by a double bracket of two pseudo-differential operato rs. These double bracket equations arose originally in the study by Brocket t of the steepest descent equations corresponding to certain least squares matching and sorting problems. We deal with some algebraic properties of th ese equations, in particular, we show that, as in the classical case, they are related to the presence of an infinite sequence of first integrals. (C) 1999 Elsevier Science B.V. All rights reserved.