Establishes large sets of Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on Z^d, extending linear and random results to nonlinear deterministic settings via a new Diophantine estimate and Bourgain's geometric lemma.
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Establishes polynomial long-time stability of polynomially weighted l2 norms for solutions of the d-dimensional nonlinear Maryland model via Birkhoff normal form.
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Anderson localized states for the quasi-periodic nonlinear Schr\"odinger equation on $\mathbb Z^d$
Establishes large sets of Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on Z^d, extending linear and random results to nonlinear deterministic settings via a new Diophantine estimate and Bourgain's geometric lemma.
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Long-time stability for nonlinear Maryland models
Establishes polynomial long-time stability of polynomially weighted l2 norms for solutions of the d-dimensional nonlinear Maryland model via Birkhoff normal form.