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Unresolved problems in the theory of integrable systems

By Vladimir Zakharov

Appears in collection : French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires

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.

Information about the video

Date of recording 6/14/17
Date of publication 6/22/17
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19182503
Cite this video Zakharov Vladimir (6/14/17). Unresolved problems in the theory of integrable systems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19182503
URL https://dx.doi.org/10.24350/CIRM.V.19182503

Domain(s)

Mathematical Physics

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

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