A rigorous derivation of the Hamiltonian structure for the nonlinear Schrödinger equation (Q2308309)

The authors consider the cubic nonlinear Schrödinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian sytsem. Inspired by the knowledge that the NLS is an effective equation for a system of interacting bosons as the particle number tends to infinity, they provide a derivation of the Hamiltonian structure. This is comprised of both a Hamiltonian functional and a weak symplectic structure, for the nonlinear Schrödinger equation from quantum many-body systems. Their geometric constructions are based on a quantized version of the Poisson structure introduced by Marsden, Morrison and Weinstein.