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We consider quasi-periodic standing wave solutions U(t, x) = exp(i(ωt−px))Ψ(x) to the one-dimensional defocusing cubic nonlinear Schrödinger equation, where we assume that Ψ : R → C is 2π−periodic. We study a constrained minimization problem associated with these solutions, and we show that solutions with minimal period of Ψ(x) strictly less than 2π cannot be minimizers, whereas locally the minimu
