Super-Nets and their hierarchy

Super-Nets and their Hierarchy

A Super-Integrable Hierarchy and Its Super-Hamiltonian Structure

It has been an important and interesting topic in soliton theory for searching for new Lax integrable or Liouville integrable systems as many as possible such that they are associated with certain evolution equations with physical meaning. The simple and efficient method to obtain continuous or discrete integrable systems was proposed Tu. Ma developed it and called it Tu scheme. By taking advan...

Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy

Enlargement of Lie super algebra B(0, 1) was given firstly. Then nonlinear super integrable couplings of the super classical Boussinesq hierarchy based upon this enlarged matrix Lie super algebra were constructed secondly. And its super Hamiltonian structures were established by using super trace identity thirdly. As its reduction, special integrable couplings of classical Boussinesq hierarchy ...

Best Fairness Hierarchy in Elementary Nets

The fairness hierarchy and conspiracies, the notions introduced by Best, are studied in the context of elementary nets. Proving that sequential as well as persistent systems are conspiracy-free, we indicate two main roots of conspiracies: distributed memory and conflicts. Using the notion of markingfairness, due to Merceron, we prove that T0-fairness + M0-fairness = T∞fairness. This result give...

Bi-Hamiltonian Structure of Super KP Hierarchy

We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator Λ = θ + ∑∞ i=−2 Uiθ , as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super W -algebra incorporating all known extended superconformal WN algebras by reduction. We also construct the super BKP hierarchy by imposing a set of an...