Proves existence of spatially exponentially localized time-periodic ground states in d-dimensional discrete NLS with delta potential and power nonlinearity, with explicit lower excitation thresholds for focusing cases and upper thresholds for defocusing cases, plus scattering below threshold.
Dodson, Global well-posedness and scattering for the mass critical nonlinear Schr¨ odinger equation with mass below the mass of the ground state , Adv
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Nonlinear discrete Schr\"odinger equations with a point defect
Proves existence of spatially exponentially localized time-periodic ground states in d-dimensional discrete NLS with delta potential and power nonlinearity, with explicit lower excitation thresholds for focusing cases and upper thresholds for defocusing cases, plus scattering below threshold.