Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation

2024/12/04 by Huabin Ge, Ge, Huabin, Bobo Hua +5
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.02947

openalex publication_date 2024/12/04 · openalex created_date 2024/12/06 · openalex updated_date 2026/07/28

Abstract

In this article, we prove the decay estimate for the discrete Schrödinger equation (DS) on the hexagonal triangulation. The l¹→ l^∞ dispersive decay rate is ⟨ t⟩^-(3)/(4), which is faster than the decay rate of DS on the 2-dimensional lattice ℤ², which is ⟨ t⟩^-(2)/(3), see [32]. The proof relies on the detailed analysis of singularities of the corresponding phase function and the theory of uniform estimates on oscillatory integrals developed by Karpushkin [15]. Moreover, we prove the Strichartz estimate and give an application to the discrete nonlinear Schrödinger equation (DNLS) on the hexagonal triangulation.

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