Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918068414840832 |
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| author | Bernier, Joackim Camps, Nicolas |
| author_facet | Bernier, Joackim Camps, Nicolas |
| contents | We consider nonlinear Schrödinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of most of the small solutions in high regularity Sobolev spaces. To this end, we develop a normal form approach designed to handle general resonant Hamiltonian partial differential equations for which it is possible to modulate the frequencies by using the initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori Bernier, Joackim Camps, Nicolas Analysis of PDEs Dynamical Systems 35B34, 35B35, 35Q55, 37K45, 37K55 We consider nonlinear Schrödinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of most of the small solutions in high regularity Sobolev spaces. To this end, we develop a normal form approach designed to handle general resonant Hamiltonian partial differential equations for which it is possible to modulate the frequencies by using the initial data. |
| title | Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori |
| topic | Analysis of PDEs Dynamical Systems 35B34, 35B35, 35Q55, 37K45, 37K55 |
| url | https://arxiv.org/abs/2402.04122 |