コロキウム

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 be also highlighted.