2010/06/24 by Rémi Carles, Éric Dumas, Eric Dumas +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #math.AP
paper · pdf · doi:10.4171/jems/350
published as Journal of the European Mathematical Society 14, 6 (2012) 1885-1921 · 33 pages
arxiv created 2010/06/24 · openalex publication_date 2012/10/10 · arxiv updated 2012/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schr¨odinger equations with gauge invariant power-law nonlinearities and nonlocal perturbations. The model includes the Davey–Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variants. Our analysis reveals a new localization phenomenon for nonlocal perturbations in the high frequency regime and allows us to infer strong instability results on the Cauchy problem in negative order Sobolev spaces, where we prove norm inflation with infinite loss of regularity by a constructive approach.