Dispersive Integrable Equations: Pathfinders in Infinite-Dimensional Hamiltonian Systems / Équations Intégrables Dispersives, Pionniers des Systèmes Hamiltoniens en Dimension Infinie

Collection Dispersive Integrable Equations: Pathfinders in Infinite-Dimensional Hamiltonian Systems / Équations Intégrables Dispersives, Pionniers des Systèmes Hamiltoniens en Dimension Infinie

Organizer(s) Gérard, Patrick ; Grava, Tamara ; Miller, Peter ; Visan, Monica

Date(s) 28/04/2025 - 02/05/2025

linked URL https://conferences.cirm-math.fr/3209.html

00:00:00 / 00:00:00

4 5

Long-time behavior for the Benjamin-Ono equation: an example

By Louise Gassot

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

Information about the video

Date of recording 29/04/2025
Date of publication 13/05/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20344203
Cite this video Gassot, Louise (29/04/2025). Long-time behavior for the Benjamin-Ono equation: an example. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20344203
URL https://dx.doi.org/10.24350/CIRM.V.20344203

Domain(s)

Analysis of PDEs

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

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

01:00:49

published on May 13, 2023

Extreme superposition: rogue waves of infinite order

By Deniz Bilman

47:14

published on May 13, 2023

Continuum Calogero–Moser models

By Thierry Laurens

58:32

published on May 13, 2023

On global well-posedness for the periodic derivative nonlinear Schrödinger equation on the torus

By Galina Perelman

45:24

published on May 13, 2023

Long-time behavior for the Benjamin-Ono equation: an example

By Louise Gassot

55:48

published on May 13, 2023

Global well posedness and soliton resolution for the half-wave maps equation with rational data

By Enno Lenzmann

Copyright Carmin.tv 2025

Give feedback