Structural properties of the noncommutative KdV recursion operator

Abstract

The present work studies structural properties of the recursion operator of the noncommutative KdV equation. As the main result, it is proved that this operator is hereditary. The notion of hereditary operators was introduced by Fuchssteiner for infinite-dimensional integrable systems, building on classical concepts from differential topology. As an illustration for the consequences of this property, it is deduced that the flows of the noncommutative KdV hierarchy mutually commute.</p