Modified scattering for the cubic Schrödinger equation on product spaces: the nonresonant case

2015/02/26 by Benoît Grébert, Eric Paturel, Grébert, Benoît +4 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1502.07699

openalex publication_date 2015/02/26 · arxiv created 2015/06/09 · arxiv updated 2015/06/10 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

We consider the cubic nonlinear Schrödinger equation on the spatial domain ℝ× \mathbbT^d, and we perturb it with a convolution potential. Using recent techniques of Hani-Pausader-Tzvetkov-Visciglia, we prove a modified scattering result and construct modified wave operators, under generic assumptions on the potential. In particular, this enables us to prove that the Sobolev norms of small solutions of this nonresonant cubic NLS are asymptotically constant.

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