Speaker 1 :  Theodoros Horikis  (University of Ioannina)
    Date & Time : May 27 (Fri.), 2022 / 10:00-10:40PM (Tokyo (JST))
                  (--> May 27 (Fri.), 2022 / 4:00-4:40PM (Greece (EEST)) )
    Title : Light meets water in nonlocal media
    Abstract : 
         Many physically different subjects can be brought together through
       their common modelling and mathematical description. Perhaps the
       most common (and rather unlike) example is water waves and
       nonlinear optics. Two systems are inextricably linked with both
       subjects: the universal Korteweg-de Vries (KdV) and nonlinear
       Schrödinger (NLS) equations. Remarkable as these systems may be,
       for several physically relevant contexts their standard form turns
       out to be an oversimplified description as it cannot model, for
       example, higher dimensionality; for instance, the
       Kadomtsev-Petviashvilli (KP) equation is used as a generalization
       of the KdV to two spatial dimensions. Furthermore, these systems
       can be reduced from one to the other, thus suggesting that
       phenomena occurring in water waves will also exist in optics. In
       fact, in this talk, we demonstrate a direct analogue of surface
       tension in optics though a nonlocal NLS equation. In particular,
       using a framework of multiscale expansions, the nonlocal NLS system
       is reduced to a KP equation, which in turn is distinguished in the
       KPI and KPII systems depending on the magnitude of the surface
       tension. Furthermore, this surface tension, the phenomenon that
       causes fluids to minimize the area they occupy, is linked to the
       physical parameters of the original nonlocal system and it is thus
       shown that nonlocality is its direct analogue. We demonstrate how
       soliton solutions and their interaction patterns, as observed in
       shallow waters, can now also be observed in optics and hence,
       shallow water wave phenomena may find their analogue in optics
       through this nonlocal NLS model in (2+1)-dimensions.