super-Hamiltonian Structures Research Articles

SUPER-BURGERS SOLITON HIERARCHY AND ITS SUPER-HAMILTONIAN STRUCTURE

A super-Burgers hierarchy and its super-Hamiltonian structure is obtained respectively based on Lie super-algebra and is associated with super-trace identity.

SUPER-DISPERSIVE LONG WAVE HIERARCHY AND ITS SUPER-HAMILTONIAN STRUCTURES

Super-dispersive long wave hierarchy is obtained by use of the Lie super-algebra B(0, 1), then the super-Hamiltonian structure of the above system is given by the associated supertrace identity. The method can be used to produce the super-Hamiltonian structures of the other superintegrable systems.

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.

Hamiltonian and super-Hamiltonian systems of a hierarchy of soliton equations

By considering an isospectral eigenvalue problem, a hierarchy of soliton equations are derived. Two types of extensions are presented by enlarging the associated spectral problem. With the aid of generalized trace identity and the super-trace identity, the Hamiltonian and super-Hamiltonian structures for the integrable extensions are established.

A Super-Soliton Hierarchy and Its Super-Hamiltonian Structure

A super-soliton hierarchy and its super-Hamiltonian structure is obtained respectively based on Lie super-algebra and associated super-trace identity.

A supertrace identity and its applications to superintegrable systems

A supertrace identity on Lie superalgebras is established. It provides a tool for constructing super-Hamiltonian structures of zero curvature equations associated with Lie superalgebras. Applications in the case of the Lie superalgebra B(0,1) present super-Hamiltonian structures of a super-AKNS soliton hierarchy and a super-Dirac soliton hierarchy.

Super Hamiltonian structure of the even order SKP hierarchy without reduction

The super Hamiltonian operator which is different from that of Manin and Radul is derived from the even order SKP hierarchy without reduction and in terms of the operator, the equation in the hierarchy is written in a Hamiltonian form.

Odd and even Poisson brackets in dynamical systems

On supermanifolds, two kinds of Poisson brackets are known to exist: even and odd. We present a general theory of even and odd super-Hamiltonian structures and apply it to a supersymmetric dynamics of one-dimensional fluid to derive an unusual symmetry between bosons and fermions.