English
Long-time behavior for the Benjamin-Ono equation: an example
Multi angle
Auteurs : Gassot, Louise (Auteur de la Conférence)
CIRM (Editeur )
35C05 - Solutions in closed form
35Q51 - Soliton-like equations
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
CIRM (Editeur )
Loading the player...
|
Résumé :
We prove that the solution to the Benjamin-Ono equation on the line, with initial data given by minus a soliton, exhibits scattering in infinite time. Our approach relies on an explicit formula for solutions with rational initial data in L2 having only simple poles. This formula is expressed as a ratio of determinants involving contour integrals. Additionally, we develop some spectral properties of the Lax operator associated with the Benjamin-Ono equation. This work is in collaboration with Elliot Blackstone, Patrick Gérard, and Peter D. Miller
Keywords : Benjamin-Ono equation; Cauchy problem; exact solutions; long-time behavior
Codes MSC : Keywords : Benjamin-Ono equation; Cauchy problem; exact solutions; long-time behavior
35C05 - Solutions in closed form
35Q51 - Soliton-like equations
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 13/05/2023 Date de captation : 29/04/2025 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : PDE Format : MP4 (.mp4) - HD Durée : 00:45:24 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-29_Gassot.mp4 
|
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.20344203Citer cette vidéo: Gassot, Louise (2025). Long-time behavior for the Benjamin-Ono equation: an example. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20344203 URI : http://dx.doi.org/10.24350/CIRM.V.20344203 |
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] Continuum Calogero–Moser models / Auteur de la Conférence Laurens, Thierry.
- [Multi angle] Extreme superposition: rogue waves of infinite order / Auteur de la Conférence Bilman, Deniz.
Bibliographie
- BLACKSTONE, Elliot, GASSOT, Louise, GÉRARD, Patrick, et al. The Benjamin-Ono initial-value problem for rational data. arXiv preprint arXiv:2410.14870, 2024. - https://doi.org/10.48550/arXiv.2410.14870
Imagette Video
