Nonlinear Waves Seminar: Gennady El
Integrable Dynamics of Soliton Gases
Gennady El
,Ìý
Date and time:Ìý
Tuesday, September 9, 2014 - 4:00pm
³¢´Ç³¦²¹³Ù¾±´Ç²Ô:Ìý
ECCR 226
´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý
Nonlinear dispersive waves, while often being successfully modeled by integrable systems (KdV, NLS, ...) can demonstrate very complex behaviours calling for a statistical description characteristic of the classical turbulence theories. There has been significant growth of interest in "integrable turbulence" recently (see e.g. V.E. Zakharov, Stud. Appl. Math. 122, 219-234 (2009)), partly due to numerous observational and experimental evidence of the presence of complex, incoherent nonlinear wave regimes in physical systems well described by integrable equations. An important section of the emerging theory of turbulence in integrable systems is the mathematical theory of soliton gases initiated by Zakharov back in 1971. In this talk I will review recent (and not-so-recent) results on the structure and dynamics of soliton gases in integrable systems. The main attention will be paid to the kinetic equation for solitons and its hydrodynamic reductions.