Bosonization and operatorial extensions of supersymmetric Korteweg-de Vries equations

摘要

We discuss the bosonization of supersymmetric KdV as a first step on the construction of operatorial extensions of that system. We obtain the hamiltonian structure of those operatorial extensions using extended Miura tranformations. We also discuss their integrability properties in terms of extended Gardner tranformations. We give explicit examples of some operatorial extensions.