English
Continuum Calogero–Moser models
Multi angle
Auteurs : Laurens, Thierry (Auteur de la Conférence)
CIRM (Editeur )
35Q55 - NLS-like equations (nonlinear Schrödinger)
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
35Q70 - PDEs in connection with mechanics of particles and systems
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3209/Slides/LAURENS.pdf
CIRM (Editeur )
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Résumé :
The focusing Continuum Calogero–Moser (CCM) equation is a completely integrable PDE that describes a continuum limit of a particle gas interacting pairwise through an inverse square potential. This system is well-posed in the scaling-critical space L2 below the mass of the soliton, but above this threshold there are solutions that blow up in finite time. In this talk, we will discuss some new and existing results about solutions below the soliton mass threshold. This is based on joint work with Rowan Killip and Monica Visan.
Keywords : nonlinear Schrödinger equations; completely integrable systems; Calogero; Moser
Codes MSC : Keywords : nonlinear Schrödinger equations; completely integrable systems; Calogero; Moser
35Q55 - NLS-like equations (nonlinear Schrödinger)
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
35Q70 - PDEs in connection with mechanics of particles and systems
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3209/Slides/LAURENS.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 13/05/2023 Date de captation : 28/04/2025 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : Analysis and its Applications ; PDE Format : MP4 (.mp4) - HD Durée : 00:47:14 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-28_Laurens.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Dispersive Integrable Equations: Pathfinders in Infinite-Dimensional Hamiltonian Systems / Équations Intégrables Dispersives, Pionniers des Systèmes Hamiltoniens en Dimension InfinieOrganisateurs de la rencontre : Gérard, Patrick ; Grava, Tamara ; Miller, Peter ; Visan, Monica Dates : 28/04/2025 - 02/05/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3209.html
Données de citation
DOI : 10.24350/CIRM.V.20344403Citer cette vidéo: Laurens, Thierry (2025). Continuum Calogero–Moser models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20344403 URI : http://dx.doi.org/10.24350/CIRM.V.20344403 |
Voir aussi
- [Multi angle] On global well-posedness for the periodic derivative nonlinear Schrödinger equation on the torus / Auteur de la Conférence Perelman, Galina.
- [Multi angle] Global well posedness and soliton resolution for the half-wave maps equation with rational data / Auteur de la Conférence Lenzmann, Enno.
- [Multi angle] Long-time behavior for the Benjamin-Ono equation: an example / Auteur de la Conférence Gassot, Louise.
- [Multi angle] Extreme superposition: rogue waves of infinite order / Auteur de la Conférence Bilman, Deniz.
Bibliographie
- KILLIP, Rowan, LAURENS, Thierry, et VISAN, Monica. Scaling-critical well-posedness for continuum Calogero-Moser models. arXiv preprint arXiv:2311.12334, 2023. - https://doi.org/10.48550/arXiv.2311.12334
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