Nonlinearization Of Two Kinds Of New Super Integrable Hierarchies

We will construct new super Dirac hierarchy and super NLS-MKd V hierarchy associated with the Lie superalgebra osp(2,2).As for the super Dirac hierarchy,we consider an explicit symmetry constraint.After substituting the constraint into finite-dimensional system,we show that the constrained system is super Hamiltonian system,and has enough integrals of motion,which are in involution in pair and functionally independent.That is to say,the constrained system are completely integrable in the Liouville sense.And as for the super NLS-MKd V hierarchy,we consider two kinds of symmetry constraints(an explicit symmetry constraint and an implicit symmetry constraint).On the one had,for the explicit symmetry constraint,we use a similar method of super Dirac hierarchy.After substituting the explicit constraint into the finite-dimensional system,we prove the constrained system is super Hamiltonian system,and are completely integrable in the Liouville sense.On the other hand,for the implicit symmetry constraint,it is necessary to introduce some appropriate new variables.Substituting the new variables and implicit symmetry constraint into the finite-dimensional system,we prove that the constrained system is also completely integrable in the sense of Liouville.