Binary Nonlinearization Of The Super Integrable Systems

In this paper,we apply binary nonlinearization to the Lax pairs and the adjoint Lax pairs for the super AKNS system,the super Dirac system and the super cKdV system.After summariz-ing the method of binary nonlinearization of the Lax pairs and the adjoint Lax pairs for classical AKNS system,Dirac system and cKdV system,we come to the following conclusion.As for the super AKNS system and the super Dirac system,we respectively propose an explicitly symmetry constraint.Under the explicit constraint,the spacial part and the temporal parts of two systems are nonlinearized into two finite-dimensional integrable super Hamiltonian systems in the Liouville sense,respectively.Specially,as for the super cKdV system,we consider a novel symmetry con-straint(the constraint is explicit for even potentials,but is implicit for odd potentials).Under the novel constraint,the spacial part and the temporal parts of the super cKdV system are nonlin-earized into two finite-dimensional super systems.Furthermore,we find that the super systems are Hamiltonian,and completely integrable in the Liouville sense.