Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy

Details Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy

1998-01-15

arxiv.org/abs/solv-int/9801019v2

J. Math. Phys. 39 (1998) 3738

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, Revtex, no figures. Minor changes, reference corrected

Scientific paper

10.1063/1.532464

We give a matrix formulation of the Hamiltonian structures of constrained KP hierarchy. First, we derive from the matrix formulation the Hamiltonian structure of the one-constraint KP hierarchy, which was originally obtained by Oevel and Strampp. We then generalize the derivation to the multi-constraint case and show that the resulting bracket is actually the second Gelfand-Dickey bracket associated with the corresponding Lax operator. The matrix formulation of the Hamiltonian structure of the one-constraint KP hierarchy in the form introduced in the study of matrix model is also discussed

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