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A method is suggested for studying the Hamiltonian structure of the nonlinear partial differential equations that can be solved by the use of the spectral transform (soliton equations). The method is applied to a new hierarchy of N+1 coupled partial differential equations related to a Schrödinger-like spectral problem. It is shown that these soliton equations are integrable Hamiltonian equations with commuting flows. For N=1 and N=2 a Miura-like transformation is computed and the corresponding modified equations are explicitly given.

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