The Cartan covering and complete integrability of the KdV-MKdV system

The coupled KdV–mKdV system arises as the classical part of one of superextensions of the KdV equation. For this system, we prove its complete integrability, i.e., existence of a recursion operator and of infinite series of symmetries. After giving a short introduction into the theory of symmetries, coverings, and the notion of Cartan-covering, the recursion operator will be constructed as a symmetry in the Cartan covering of the KdV–mKdV system.