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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2010
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1010.5173 |
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| _version_ | 1866914585672417280 |
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| author | Carles, Remi Faou, Erwan |
| author_facet | Carles, Remi Faou, Erwan |
| contents | We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus. For special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. The proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two-dimensional discrete dynamical system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1010_5173 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Energy cascades for NLS on the torus Carles, Remi Faou, Erwan Analysis of PDEs Mathematical Physics Primary 35Q55, Secondary 35C20, 37K55 We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus. For special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. The proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two-dimensional discrete dynamical system. |
| title | Energy cascades for NLS on the torus |
| topic | Analysis of PDEs Mathematical Physics Primary 35Q55, Secondary 35C20, 37K55 |
| url | https://arxiv.org/abs/1010.5173 |