Supersymmetric Bi-Hamiltonian Systems

We construct super Hamiltonian integrable systems within the theory of supersymmetric Poisson vertex algebras (SUSY PVAs). provide a powerful tool for understanding SUSY PVAs called master formula. attach some Lie superalgebraic data to generalized W-algebra and show that it is equipped with two compatible PVA brackets. reformulate these brackets in terms odd differential operators obtain bi-Hamiltonian hierarchies after performing analog Drinfeld–Sokolov reduction on operators. As an example, system constructed from $${\mathfrak {g}}=\mathfrak {osp}(2|2)$$ .