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| HAL: hal-00528792, version 2 |
| DOI: 10.3934/dcds.2012.32.2063 |
| Detailed view |  Export this paper |
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| Discrete and Continuous Dynamical Systems 32, 6 (2012) 2063-2077 |
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| Available versions: | v1 (2010-10-23) | v2 (2010-10-23) |
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| Energy cascades for NLS on $\T^d$ |
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| Rémi Carles 1Erwan Faou 2, 3 |
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| (2012) |
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| 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. |
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| 1: | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et techniques |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | IPSO (INRIA - IRMAR) |
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CNRS : UMR6074 – INRIA – Université de Rennes 1 |
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| Analyse numérique |
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| Subject | : | Mathematics/Analysis of PDEs |
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| hal-00528792, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00528792 | |
| oai:hal.archives-ouvertes.fr:hal-00528792 | |
| From: Rémi Carles | |
| Submitted on: Saturday, 23 October 2010 11:11:55 | |
| Updated on: Monday, 17 June 2013 15:06:01 | |
