The hamiltonian structures of the KP hierarchy

N = 2 super W∞ algebra and its nonlinear realization through super KP formulation

“…Notice that similar situation has been observed in the case of Gelfand Dikii bracket of second kind for the bosonic KP hierarchy [8].…”

“…The Poisson bracket algebra, we have obtained following Gelfand Dikii method, gives rise to a nonlinear realization of super W ∞ algebra. In alalogy with bosonic KP hierarchy [8] we believe this algebra may be realized as universal super W ∞ algebra.…”

“…However, owing to the ambiguity inherent in the large n limits, a nonlinear realization of universal W algebra,Ŵ ∞ has been constructed and identified with the second Hamiltonian structure of KP hierarchy [8].…”

On two-current realization of KP hierarchy

“…Taking this into account one realizes [20,12] that a further structure is required. Following [21] we will call this structure a Drinfeld-Sokolov (DS) bracket [22] and define it as…”

“…In fact DS bracket is coordinated with both Ω (0) and Ω (1) linear bracket structures. The second Hamiltonian structure compatible with Lenard relations is given by [20]:…”