The generalized KP hierarchy, Hamiltonian structure and non-abelian two-boson realization

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A matrix generalization of the KP hierarchy is formulated with the help of matrix pseudodifferential operator. While the first Gelfand-Dickey bracket is found to be a non-abelian generalization of the W1 + ∞ algebra, the corresponding second one is found to be nonlinear and nonlocal. Finally, the constrained system corresponding to this hierarchy is considered. In a particular case the resulting equations turn out to be a multicomponent generalization of the Nonlinear Schrödinger equation. It is also demonstrated that a matrix generalization of the usual two-boson realization exists in the present case.