Speaker 2 :  Amin Chabchoub  (Kyoto University / University of Sydney)
    Date & Time : July 16th (Fri.), 2021 / 10:50-11:30PM (Tokyo (JST))
    Title : Soliton and Breather Hydrodynamics
    Abstract : 
         The dynamics of water waves can be described within the framework of weakly
       nonlinear evolution equations such as the Korteweg-de Vries equation (KdV) in 
       shallow-water and the nonlinear Schrödinger equation (NLS) in intermediate 
       water depth as well as deep-water regime. Both, KdV and NLS are physically very 
       rich and can be for instance used to study the fundamental principles of 
       nonlinear dynamics such as the Fermi-Pasta-Ulam recurrence. By applying 
       mathematical techniques such as the Darboux transformation or the inverse 
       scattering transform, these integrable evolution equations provide exact models 
       that can be studied analytically, numerically and in controlled in laboratory 
       environments. Lately, the emergence of rogue waves in different nonlinear 
       dispersive media has attracted scientific interest. Indeed, one possible 
       explanation for their formation is provided by the modulation instability. 
       This latter instability can be deterministically discussed within the context 
       of exact NLS breather solutions, such as fundamental Akhmediev- or 
       Peregrine-type breathers. Recent experimental studies on solitons and breathers
       in water wave tanks will be presented while novel insights of the modulation 
       instability also in directional wave fields will be discussed. The relevance 
       of such fundamental coherent waves across disciplines will also be highlighted.