Randomized trial finds large sets of Anderson localized states for nonlinear Schrödinger equations, suggesting new insights into localization phenomena.
We establish large sets of Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on Z d Zᵈ double struck upper Z Superscript d , thus extending Anderson localization from the linear (cf. Bourgain [Geom. Funct. Anal., 17(3):682–706, 2007]) to a nonlinear setting, and from the random (cf. Bourgain-Wang [J. Eur. Math. Soc., 10(1):1–45, 2008]) to a deterministic setting. Among the main ingredients are a new Diophantine estimate of quasi-periodic functions in arbitrary-dimensional phase space, and the application of Bourgain’s geometric lemma in [Geom. Funct. Anal., 17(3):682–706, 2007].
No takes yet. Share an insight, caveat, or question.
Shi et al. (2026) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: