2011/02/28 by Xuwen Chen · 33 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Anisotropy #Hierarchy #Nonlinear Waves and Solitons #Nonlinear system #Quadratic equation #Quantum Mechanics and Non-Hermitian Physics #Uniqueness #Work (physics) #math-ph #math.AP #math.MP #msc:35A02 #msc:35A23 #msc:35B45 #msc:35Q55 #msc:81Q05 #msc:81V70
paper · pdf · doi:10.1016/j.matpur.2012.02.003
published in Journal de Mathématiques Pures et Appliquées 98(4), 450-478 (Elsevier BV) · v6, 32 pages. Added an algebraic explanation of the generalized lens transform using the metaplectic representation. Accepted to appear in Journal de Mathématiques Pures et Appliquées. Comments are welcomed
arxiv created 2012/01/08 · openalex publication_date 2012/02/28 · arxiv updated 2012/09/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the 2d and 3d many body Schrödinger equations in the presence of anisotropic switchable quadratic traps. We extend and improve the collapsing estimates in Klainerman-Machedon [24] and Kirkpatrick-Schlein-Staffilani [23]. Together with an anisotropic version of the generalized lens transform in Carles [3], we derive rigorously the cubic NLS with anisotropic switchable quadratic traps in 2d through a modified Elgart-Erdös-Schlein-Yau procedure. For the 3d case, we establish the uniqueness of the corresponding Gross-Pitaevskii hierarchy without the assumption of factorized initial data.