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

1 5

Extreme superposition: rogue waves of infinite order

By Deniz Bilman

The focusing nonlinear Schrödinger equation serves as a universal model for the amplitude of a wave packet in a general one-dimensional weakly-nonlinear and strongly-dispersive setting that includes water waves and nonlinear optics as special cases. Rogue waves of infinite order are a novel family of solutions of the focusing nonlinear Schr¨odinger equation that emerge universally in a particular asymptotic regime involving a large-amplitude and near-field limit of a broad class of solutions of the same equation. In this talk, we will present several recent results on the emergence of these special solutions along with their interesting asymptotic and exact properties. Notably, these solutions exhibit anomalously slow temporaldecay and are connected to the third Painlev´e equation. Finally, we will extend the emergence of rogue waves of infinite order to the first several flows of the AKNS hierarchy — allowing for arbitrarily many simultaneous flows — and report on recent work regarding their space-time asymptotic behavior under a general flow from the hierarchy.

Information about the video

Date of recording 28/04/2025
Date of publication 13/05/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20344003
Cite this video Bilman, Deniz (28/04/2025). Extreme superposition: rogue waves of infinite order. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20344003
URL https://dx.doi.org/10.24350/CIRM.V.20344003

Domain(s)

Analysis of PDEs

Bibliography

BILMAN, Deniz et MILLER, Peter D. General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation. arXiv preprint arXiv:2408.05390, 2024. - https://doi.org/10.48550/arXiv.2408.05390

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