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Continuum Calogero–Moser models
Multi angle
Authors : Laurens, Thierry (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/RepOrga/3209/Slides/LAURENS.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/3209/Slides/LAURENS.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/05/2023 Conference Date : 28/04/2025 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : Analysis and its Applications ; PDE Format : MP4 (.mp4) - HD Video Time : 00:47:14 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-28_Laurens.mp4 
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Information on the Event
Event Title : Dispersive Integrable Equations: Pathfinders in Infinite-Dimensional Hamiltonian Systems / Équations Intégrables Dispersives, Pionniers des Systèmes Hamiltoniens en Dimension InfinieEvent Organizers : Gérard, Patrick ; Grava, Tamara ; Miller, Peter ; Visan, Monica Dates : 28/04/2025 - 02/05/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3209.html
Citation Data
DOI : 10.24350/CIRM.V.20344403Cite this video as: 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 |
See Also
- [Multi angle] On global well-posedness for the periodic derivative nonlinear Schrödinger equation on the torus / Author of the conference Perelman, Galina.
- [Multi angle] Global well posedness and soliton resolution for the half-wave maps equation with rational data / Author of the conference Lenzmann, Enno.
- [Multi angle] Long-time behavior for the Benjamin-Ono equation: an example / Author of the conference Gassot, Louise.
- [Multi angle] Extreme superposition: rogue waves of infinite order / Author of the conference Bilman, Deniz.
Bibliography
- 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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