Short Lenard Chains and Integrable Systems

It is well-known that certain classes of integrable PDE's are organized in hierarchies, called Lenard chains, defined by torsionless recursion operators. This property is lost in the dispersionless limit. In this case the notion of short Lenard chain seems to be more appropriate. In the talk I will discuss the interplay of this notion with the theory of Frobenius manifolds, and I will present a concrete example, related to a former work by Gepner.