Abstract
Quantizations of \(C^\infty (T*\mathbb{R}^1 )\) parametrize realizations of universal dynamical systems whose integrability is proved and hamiltonian form established. For the case of the Moyal bracket, the analogs of the KdV equation, Boussinesq system, the first nontrivial flow in the KP hierarchy, and the KP equation, are computed.
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