Equations of Lax type with several brackets

Resumen

In the present paper we introduce a new hierarchy, each equation of which is defined by several brackets of two pseudodifferential operators.  We deal with some algebraic properties of these equations. In particular, we show that, as in the classic case, they are related to the presence of an infinite sequence of first integrals. A new version of the Zakharov-Shabat type equations is proved. Formal solutions of this hierarchy are constructed using a “several brackets bilinear identity”