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Long-time behavior for the Benjamin-Ono equation: an example
Multi angle
Authors : Gassot, Louise (Author of the conference)
CIRM (Publisher )
35C05 - Solutions in closed form
35Q51 - Soliton-like equations
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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.)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/05/2023 Conference Date : 29/04/2025 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : PDE Format : MP4 (.mp4) - HD Video Time : 00:45:24 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-29_Gassot.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.20344203Cite this video as: 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 |
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] Continuum Calogero–Moser models / Author of the conference Laurens, Thierry.
- [Multi angle] Extreme superposition: rogue waves of infinite order / Author of the conference Bilman, Deniz.
Bibliography
- 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
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