## The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems.(English)Zbl 1200.35244

Summary: 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 super-symmetry manifold $$\mathbb{R}^{4N|2N}$$ with the corresponding dynamical variables $$x$$ and $$t_n$$. The integrals of motion required for Liouville integrability are explicitly given.

### MSC:

 35Q51 Soliton equations 35B06 Symmetries, invariants, etc. in context of PDEs 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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### References:

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