On the variational characterization of quasi-periodic standing waves of the nonlinear Schrödinger equation

Sammanfattning: 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 minimum is obtained among those solutions with minimal period 2π.