The cubic NLS Hamiltonian structure is the pullback of a many-body Gross-Pitaevskii hierarchy Hamiltonian structure along a Poisson morphism.
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A Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schr\"odinger Equation
The cubic NLS Hamiltonian structure is the pullback of a many-body Gross-Pitaevskii hierarchy Hamiltonian structure along a Poisson morphism.