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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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