Resumen de Equations of Lax type with a triple bracket

Raúl Felipe, Raúl Velásquez

• Equations with several brackets arose originally in the works of Brockett [2], [3] (for ordinary differential equations) and Felipe [5] (for partial differential equations) of double bracket equations of Lax type. The purpose of this note is to study triple bracket equations of the form: ?L / ?t = [L,[L,[L,P]]]. 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. We also exhibit some new integrable systems.