Abstract
It is well known that soliton equations can be written in Lax form, where the bracket of two linear differential (n-KdV) or pseudo-differential (KP) operators appears. In this work, we introduce a new hierarchy; each equation of which is defined by a double bracket of two pseudo-differential operators. These double bracket equations arose originally in the study by Brockett of the steepest descent equations corresponding to certain least squares matching and sorting problems. We deal with some algebraic properties of these equations, in particular, we show that, as in the classical case, they are related to the presence of an infinite sequence of first integrals.
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