Back to Search
Start Over
Anderson localized states for the quasi-periodic nonlinear Schr\'odinger equation on $\mathbb Z^d$
- Publication Year :
- 2024
-
Abstract
- We establish large sets of Anderson localized states for the quasi-periodic nonlinear Schr\"odinger equation on $\mathbb Z^d$, thus extending Anderson localization from the linear (cf. Bourgain [GAFA 17(3), 682--706, 2007]) to a nonlinear setting, and the random (cf. Bourgain-Wang [JEMS 10(1), 1--45, 2008]) to a deterministic setting. Among the main ingredients are a new Diophantine estimate of quasi-periodic functions in arbitrarily dimensional phase space, and the application of Bourgain's geometric lemma in [GAFA 17(3), 682--706, 2007].<br />Comment: Comments welcome, 49 pages. arXiv admin note: substantial text overlap with arXiv:2306.00513
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.17513
- Document Type :
- Working Paper