Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910730636230656 |
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| author | Ge, Huabin Hua, Bobo Jia, Longsong Zhou, Puchun |
| author_facet | Ge, Huabin Hua, Bobo Jia, Longsong Zhou, Puchun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation Ge, Huabin Hua, Bobo Jia, Longsong Zhou, Puchun Analysis of PDEs 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. |
| title | Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.02947 |