RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars





You may need the following programs to see the files








Steklov Mathematical Institute Seminar
May 21, 2020 16:00, Moscow, online
 


Are Equations of Free-Surface Hydrodynamics on Deep Water Integrable?

V. E. Zakharovabc

a P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow
b University of Arizona
c Skolkovo Institute of Science and Technology
Video records:
MP4 952.2 Mb
Materials:
Adobe PDF 15.7 Mb

Number of views:
This page:767
Video files:290
Materials:60
Youtube Video:

V. E. Zakharov


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке



Abstract: We show that the Euler equations describing the unsteady potential flow of a two-dimensional deep fluid with a free surface in the absence of gravity and surface tension can be integrated exactly under a special self-similar choice of boundary conditions at infinity. Problem of exact integrability of liquid with natural boundary conditions remains open although there exist analytical and numerical arguments supporting this conjecture, in particular, existence of indefinite number (depending on the initial conditions) of commuting integrals of motion. Another strong argument is the exact cancellation of coefficients of non-trivial four wave interactions. This cancellation explains strong slowdown of stochastisation process observed in numerical experiments in the 70-ies of the previous century. Modern experiments show long existence of breather which decays in short time for non-integrable case. Proof of integrability of deep water equations would be a discovery of a completely new class of integrable systems.

Materials: slides.pdf (15.7 Mb)

* 505 682 9814 Password: 248481

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020