English
Unresolved problems in the theory of integrable systems
Post-edited
Auteurs : Zakharov, Vladimir (Auteur de la Conférence)
CIRM (Editeur )
35Q53 - KdV-like (Korteweg-de Vries) equations
35Q55 - NLS-like equations (nonlinear Schrödinger)
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
76B15 - Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76Fxx - Turbulence
35C08 - Soliton solutions of PDE
35C07 - Traveling wave solutions of PDE
CIRM (Editeur )
Résumé :
In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed in the talk.
Codes MSC : 1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed in the talk.
35Q53 - KdV-like (Korteweg-de Vries) equations
35Q55 - NLS-like equations (nonlinear Schrödinger)
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
76B15 - Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76Fxx - Turbulence
35C08 - Soliton solutions of PDE
35C07 - Traveling wave solutions of PDE
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 22/06/17 Date de captation : 14/06/17 Sous collection : Research talks arXiv category : Mathematical Physics Domaine : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 00:55:47 Audience : Researchers Download : https://videos.cirm-math.fr/2017-06-14_Zakharov.mp4 
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Informations sur la Rencontre
Nom de la rencontre : French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéairesOrganisateurs de la rencontre : Carles, Rémi ; Holmer, Justin ; Roudenko, Svetlana Dates : 12/06/17 - 16/06/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1510.html
Données de citation
DOI : 10.24350/CIRM.V.19182503Citer cette vidéo: Zakharov, Vladimir (2017). Unresolved problems in the theory of integrable systems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19182503 URI : http://dx.doi.org/10.24350/CIRM.V.19182503 |
Voir aussi
- [Multi angle] The wave equation on a model convex domain revisited / Auteur de la Conférence Planchon, Fabrice.
- [Multi angle] Dynamics of almost parallel vortex filaments / Auteur de la Conférence Banica, Valeria.
- [Multi angle] Solitons vs collapses / Auteur de la Conférence Kuznetsov, Evgenii.
- [Multi angle] Dispersive waves in novel 2d media; Honeycomb structures, edge states and the strong binding regime / Auteur de la Conférence Weinstein, Michael.
- [Multi angle] Interactions of solitary waves for the nonlinear Schrödinger equations / Auteur de la Conférence Martel, Yvan.
- [Multi angle] Soliton resolution for derivative NLS equation / Auteur de la Conférence Sulem, Catherine.
Bibliographie
- Dyachenko, S.A., Zakharov, D.V., & Zakharov, V.E. (2016). Primitive potentials and bounded solutions of the KdV equation. Physica D, 333, 148-156 - https://doi.org/10.1016/j.physd.2016.04.002
- Zakharov, D.V., & Zakharov, V.E., & Dyachenko, S.A. (2016). Non-periodic one-dimensional ideal conductors and integrable turbulence. Physical Letters A, 380(46), 3881-3885 - https://doi.org/10.1016/j.physleta.2016.09.040
- Zakharov, D.V., Dyachenko, S.A., & Zakharov, V.E. (2016). Bounded solutions of KdV and non periodic one-gap potentials in quantum mechanics. Letters in Mathematical Physics, 106(6). 731-740 - http://dx.doi.org/10.1007/s11005-016-0838-6
