2022/05/29 by Avy Soffer, Xiaoxu Wu, Soffer, Avy +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2205.14765
openalex publication_date 2022/05/29 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
We construct solutions of Schrödinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solutions are global, with non-zero L2 norms, and are stable. As such they are not of the standard asymptotic decomposition of linear waves and localized waves. Such weakly localized solutions were expected in view of previous works \citeLiu-Sof1,Liu-Sof2 on the large time behavior of general dispersive equations. It is shown that one can associate a scattering channel to such solutions, with the dilation operator as the asymptotic ``Hamiltonian''.