The nonlinear Schrödinger equation with white noise dispersion on quantum graphs

2019/05/28 by Iulian Cîmpean, Cîmpean, Iulian, Andreea Grecu +1
Mathematics · #34B45 #35J10 #35P05 #35Q55 (secondary) #60H15 (primary) #81Q35 #81U30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34B45 #msc:35J10 #msc:35P05 #msc:35Q55 #msc:60H15 #msc:81Q35 #msc:81U30

paper · pdf · doi:10.48550/arxiv.1905.11708

32 pages, 4 figures

openalex publication_date 2019/05/28 · arxiv created 2019/11/12 · arxiv updated 2019/11/13 · openalex created_date 2025/11/01 · openalex updated_date 2026/07/28

Abstract

We show that the nonlinear Schrödinger equation (NLSE) with white noise dispersion on quantum graphs is globally well-posed in L² once the free deterministic Schrödinger group satisfies a natural L¹-L^∞ decay, which is verified in many examples. Also, we investigate the well-posedness in the energy domain in general and in concrete situations, as well as the fact that the solution with white noise dispersion is the scaling limit of the solution to the NLSE with random dispersion.

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