The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems

Details The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems

2009-10-16

arxiv.org/abs/0910.3080v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14,pages, to appear in Chinses Annals of Mathematics

Scientific paper

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the supersymmetry manifold $R^{4N|2N}$ with the corresponding dynamical variables $x$ and $t_n$. The integrals of motion required for Liouville integrability are explicitly given.

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