Modified Scattering of Cubic Nonlinear Schrödinger Equation on Rescaled Waveguide Manifolds

2022/07/15 by Bobby L. Wilson, Xueying Yu, Wilson, Bobby +1
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2207.07248

openalex publication_date 2022/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use modified scattering theory to demonstrate that small-data solutions to the cubic nonlinear Schrödinger equation on rescaled waveguide manifolds, ℝ × \mathbbT^d for d≥ 2, demonstrate boundedness of Sobolev norms as well as weak instability.

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