2017/02/07 by Valeria Banica, Luis Vega, Banica, Valeria +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1702.01947
openalex publication_date 2017/02/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this note we consider the 1-D cubic Schr "odinger equation with data given\nas small perturbations of a Dirac-\δ function and some other related\nequations. We first recall that although the problem for this type of data is\nill-posed one can use the geometric framework of the Schr "odinger map to\ndefine the solution beyond the singularity time. Then, we find some natural and\nwell defined geometric quantities that are not regular at time zero. Finally,\nwe make a link between these results and some known phenomena in fluid\nmechanics that inspired this note.\n