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SUMMARY:Resonant dispersive shock waves in nonlinear optics and shallow wa
 ter waves - Saleh Baqer (Kuwait University)
DTSTART:20221208T110000Z
DTEND:20221208T113000Z
UID:TALK183800@talks.cam.ac.uk
DESCRIPTION:Dispersive hydrodynamics\, mathematical models formulated by h
 yperbolic conservation laws with dispersive corrections\, govern fluid or 
 fluid-like phenomena that naturally emerge in media whose dissipative effe
 ct (e.g.\, viscosity) is negligible or non-existent relative to wave dispe
 rsion. The framework of dispersive hydrodynamics possesses a plethora of n
 onlinear dispersive wave phenomena\, including solitary waves and dispersi
 ve shocks waves (DSWs). This talk focuses on the latter wave phenomenon ar
 ising in two contexts: nonlocal nonlinear medium of defocusing nematic liq
 uid crystals and shallow water waves with surface tension. In nematic liqu
 id crystals\, distinct non-classical DSW regimes are generated from discon
 tinuous initial conditions for the optical field and are resonant due to t
 he effect of non-convex dispersion\, resulting in a resonant radiation pro
 pagating ahead of the DSW itself. The classical DSW structure disappears a
 nd a Whitham shock emerges as the initial jumps become sufficiently large.
  Analytical methods based on Whitham modulation theory and asymptotic tech
 niques are used to determine solutions for these DSW regimes. The transiti
 on effect from the nonlocal (low power) to local (high power) limits will 
 also be considered. In the end of the talk\, a particular non-classical re
 sonant shallow water DSW regime\, so-called Cross-over DSW (CDSW)\, govern
 ed by Kawahara and extended KdV equations will be discussed. The analytica
 l solutions obtained are verified via numerical solutions and excellent ag
 reement is found.\nCo-authors: names and affiliations: Noel F. Smyth (Univ
 ersity of Edinburgh)\, Dimitri Frantzeskakis (National and Kapodistrian Un
 iversity of Athens)\, Theodoros Horikis (University of Ioannina)\, Tim Mar
 chant (University of Melbourne)&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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