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

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.