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Integrable couplings of the multi-component Dirac hierarchy and its Hamiltonian structure. (English) Zbl 1221.37130
The authors obtain multi-component integrable couplings of the Dirac hierarchy by using the vector loop algebra \(\widetilde G_M\). Then, according to the quadratic-form identity, the Hamiltonian structure of the above system is presented.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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