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arXiv · 2412.02947

Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation

Huabin Ge·Bobo Hua·Longsong Jia·Puchun Zhou
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Abstract

In this article, we prove the decay estimate for the discrete Schrödinger equation (DS) on the hexagonal triangulation. The $l^1\rightarrow l^\infty$ dispersive decay rate is $\left\langle t\right\rangle^{-\frac{3}{4}}$, which is faster than the decay rate of DS on the 2-dimensional lattice $\mathbb{Z}^2$, which is $\left\langle t\right\rangle^{-\frac{2}{3}}$, 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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Huabin Ge, Bobo Hua, Longsong Jia, Puchun Zhou. 2024-12-06. Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation. https://arxiv.org/abs/2412.02947

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