Modified scattering for the cubic Schrödinger equation on Diophantine waveguides
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916395444338688 |
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| author | Camps, Nicolas Staffilani, Gigliola |
| author_facet | Camps, Nicolas Staffilani, Gigliola |
| contents | We consider the cubic Schrödinger equation posed on product spaces subject to a generic Diophantine condition. Our analysis shows that the small-amplitude solutions undergo modified scattering to an effective dynamics governed by some interactions that do not amplify the Sobolev norms. This is in sharp contrast with the infinite energy cascade scenario observed by Hani--Pausader--Tzvetkov--Visciglia in the absence of Diophantine conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified scattering for the cubic Schrödinger equation on Diophantine waveguides Camps, Nicolas Staffilani, Gigliola Analysis of PDEs 35B40 We consider the cubic Schrödinger equation posed on product spaces subject to a generic Diophantine condition. Our analysis shows that the small-amplitude solutions undergo modified scattering to an effective dynamics governed by some interactions that do not amplify the Sobolev norms. This is in sharp contrast with the infinite energy cascade scenario observed by Hani--Pausader--Tzvetkov--Visciglia in the absence of Diophantine conditions. |
| title | Modified scattering for the cubic Schrödinger equation on Diophantine waveguides |
| topic | Analysis of PDEs 35B40 |
| url | https://arxiv.org/abs/2404.16817 |