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Unresolved problems in the theory of integrable systems
Post-edited
Authors : Zakharov, Vladimir (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 22/06/17 Conference Date : 14/06/17 Subseries : Research talks arXiv category : Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:55:47 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-06-14_Zakharov.mp4 
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Information on the Event
Event Title : French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéairesEvent Organizers : Carles, Rémi ; Holmer, Justin ; Roudenko, Svetlana Dates : 12/06/17 - 16/06/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1510.html
Citation Data
DOI : 10.24350/CIRM.V.19182503Cite this video as: 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 |
See Also
- [Multi angle] The wave equation on a model convex domain revisited / Author of the conference Planchon, Fabrice.
- [Multi angle] Dynamics of almost parallel vortex filaments / Author of the conference Banica, Valeria.
- [Multi angle] Solitons vs collapses / Author of the conference Kuznetsov, Evgenii.
- [Multi angle] Dispersive waves in novel 2d media; Honeycomb structures, edge states and the strong binding regime / Author of the conference Weinstein, Michael.
- [Multi angle] Interactions of solitary waves for the nonlinear Schrödinger equations / Author of the conference Martel, Yvan.
- [Multi angle] Soliton resolution for derivative NLS equation / Author of the conference Sulem, Catherine.
Bibliography
- 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
