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

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

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

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

00:00:00 / 00:00:00

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Extreme superposition: rogue waves of infinite order

De 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.

Informations sur la vidéo

Date de captation 28/04/2025
Date de publication 13/05/2023
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20344003
Citer cette vidéo 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

Domaine(s)

Equations aux dérivées partielles

Bibliographie

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

Codes MSC

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