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Fédération de recherche Mathématiques des Pays de Loire |  |
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Fédération de recherche Mathématiques des Pays de Loire | |
| HAL : hal-00681730, version 1 |
| arXiv : 1203.6183 |
| DOI : 10.1007/s00211-012-0491-7 |
| Fiche détaillée |  Récupérer au format |
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| Numerische Mathematik (2012) DOI 10.1007/s00211-012-0491-7 |
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| Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation |
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| Dario Bambusi 1Erwan Faou 2, 3 |
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| (2012) |
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| In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schrödinger equation on the real line. More precisely, we consider a symplectic time splitting integrator applied to a discrete nonlinear Schrödinger equation with additional Dirichlet boundary conditions on a large interval. We give conditions ensuring the existence of a numerical soliton which is close in energy norm to the continuous soliton. Such result is valid under a CFL condition between the time and space stepsizes. Furthermore we prove that if the initial datum is symmetric and close to the continuous soliton, then the associated numerical solution remains close to the orbit of the continuous soliton for very long times. |
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| 1 : | Dipartimento de Matematica [Milano] |
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Università degli studi di Milano |
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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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| 4 : | Laboratoire de Mathématiques Jean Leray (LMJL) |
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CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes |
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| Analyse numérique |
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| Domaine | : | Mathématiques/Analyse numérique |
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| Discrete nonlinear Schrödinger equation – Numerical soliton – Stability – Backward error analysis – Modified Hamiltonian |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00681730, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00681730 | |
| oai:hal.archives-ouvertes.fr:hal-00681730 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Jeudi 22 Mars 2012, 11:21:43 | |
| Dernière modification le : Jeudi 17 Janvier 2013, 18:00:07 | |
