New Conservation Laws and Energy Cascade for 1d Cubic NLS and the Schrödinger map

2023/03/15 by Valeria Banica, Luis Vega, Banica, Valeria +1
Engineering · Mathematics · Physics and Astronomy · #35B44 #35Bxx #35Q35 #35Q55 #76Fxx #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2303.08696

openalex publication_date 2023/03/15 · openalex created_date 2023/03/18 · openalex updated_date 2026/07/28

Abstract

We review some recent results concerning the Initial Value Problem of 1d-cubic non-linear Schrödinger equation (NLS) and other related systems as the Schrödinger Map. For the latter we prove the existence of a cascade of energy. Finally, some new examples of the Talbot effect at the critical level of regularity are given.

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