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Resonant Hamiltonian systems associated to the one-dimensional nonlinear Schrödinger equation with harmonic trapping
We study two resonant Hamiltonian systems on the phase space L2(R→C): the quintic one-dimensional continuous resonant equation, and a cubic resonant system that has appeared in the literature as a modified scattering limit for an NLS equation with cigar shaped trap. We prove that these systems approximate the dynamics of …