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We study the continuous resonant (CR) equation which was derived in [8] as the large-box limit of the cubic nonlinear Schrödinger equation in the small nonlinearity (or small data) regime. We first show that the system arises in another natural way, as it also corresponds to the resonant cubic Hermite–Schrödinger equation (NLS with harmonic trapping). We then establish that the basis of special Hermite...
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