2023/02/24 by Yunyan Yang, Liang Zhao, Yang, Yunyan +1 · 4 citations
Mathematics · Physics and Astronomy · #35A15 #35Q55 #35R02 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Applied mathematics #Constraint (computer-aided design) #Discrete mathematics #FOS: Mathematics #Finite graph #Geometry #Graph #Limit (mathematics) #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Schrödinger equation
paper · pdf · doi:10.48550/arxiv.2302.12585
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We are concerned with the nonlinear Schrödinger equation with an L2 mass constraint on both finite and locally finite graphs and prove that the equation has a normalized solution by employing variational methods. We also pay attention to the behaviours of the normalized solution as the mass constraint tends to 0+ or +∞ and give clear descriptions of the limit equations. Finally, we provide some numerical experiments on a finite graph to illustrate our theoretical results.