Super Integrable Hierarchy Research Articles

Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures

We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.

Conservation laws and self-consistent sources for a super integrable equation hierarchy

In this paper, a super integrable equation hierarchy is considered based on a Lie superalgebra and supertrace identity. Then, a super integrable equation hierarchy with self-consistent sources is established. Furthermore, we introduce two variables F and G to construct conservation laws of the super integrable equation hierarchy and the first two conserved densities and fluxes are listed. It would be specially mentioned that the Fermi variables play an important role in super integrable systems which is different from the ordinary integrable systems.

Integrable hierarchies related to the Kuper-CH spectral problem

In this paper, from a given Kuper-CH spectral problem, we propose two kinds of super integrable hierarchies. One is the Kuper-CH hierarchy, the other is the generalized Kuper-Harry-Dym hierarchy. Moreover, we construct their zero curvature representations and super-bi-Hamiltonian structures.

Two super-integrable hierarchies and their super-Hamiltonian structures

Two Lie super algebras are constructed from which we establish two super-isospectral problems. Under the frame of the zero curvature equations, the super-GJ hierarchy and the super-Yang hierarchy are presented respectively. Meanwhile, their super-Hamiltonian structures are obtained by using super-trace identity.

SUPER INTEGRABLE HIERARCHY AND SUPER HAMILTONIAN STRUCTURES ASSOCIATED WITH GUO HIERARCHY

A Lie superalgebra is constructed from which establishes an isospectral problems. By solving the zero curvature equation, a resulting super hierarchies of the Guo hierarchy are obtained. By making use of the super identity, the Hamiltonian structures of the above super integrable hierarchies are generated, this method can be used to other superhierarchy.

Two types of Lie super-algebra for the super-integrable Tu-hierarchy and its super-Hamiltonian structure

Two different Lie super-algebras are constructed which establish two isospectral problems. Under the frame of the zero curvature equations, the corresponding super-integrable hierarchies of the Tu-hierarchy are obtained. By making use of the super-trace identity, the super-Hamiltonian structures of the above integrable hierarchies are generated, which are Liouville integrable.