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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For almost all potentials V, the derivative nonlinear Schrödinger equation on the torus admits an almost-periodic solution.
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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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On the construction of almost periodic solutions for the derivative nonlinear Schr\"odinger equation
For almost all potentials V, the derivative nonlinear Schrödinger equation on the torus admits an almost-periodic solution.