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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Resonant dispersive shock waves in nonlinear optic
s and shallow water waves - Saleh Baqer (Kuwait Un
iversity)
DTSTART;TZID=Europe/London:20221208T110000
DTEND;TZID=Europe/London:20221208T113000
UID:TALK183800AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183800
DESCRIPTION:Dispersive hydrodynamics\, mathematical models for
mulated by hyperbolic conservation laws with dispe
rsive corrections\, govern fluid or fluid-like phe
nomena that naturally emerge in media whose dissip
ative effect (e.g.\, viscosity) is negligible or n
on-existent relative to wave dispersion. The frame
work of dispersive hydrodynamics possesses a pleth
ora of nonlinear dispersive wave phenomena\, inclu
ding solitary waves and dispersive shocks waves (D
SWs). This talk focuses on the latter wave phenome
non arising in two contexts: nonlocal nonlinear me
dium of defocusing nematic liquid crystals and sha
llow water waves with surface tension. In nematic
liquid crystals\, distinct non-classical DSW regim
es are generated from discontinuous initial condit
ions for the optical field and are resonant due to
the effect of non-convex dispersion\, resulting i
n a resonant radiation propagating ahead of the DS
W itself. The classical DSW structure disappears a
nd a Whitham shock emerges as the initial jumps be
come sufficiently large. Analytical methods based
on Whitham modulation theory and asymptotic techni
ques are used to determine solutions for these DSW
regimes. The transition effect from the nonlocal
(low power) to local (high power) limits will also
be considered. In the end of the talk\, a particu
lar non-classical resonant shallow water DSW regim
e\, so-called Cross-over DSW (CDSW)\, governed by
Kawahara and extended KdV equations will be discus
sed. The analytical solutions obtained are verifie
d via numerical solutions and excellent agreement
is found.\nCo-authors: names and affiliations: Noe
l F. Smyth (University of Edinburgh)\, Dimitri Fra
ntzeskakis (National and Kapodistrian University o
f Athens)\, Theodoros Horikis (University of Ioann
ina)\, Tim Marchant (University of Melbourne)
\;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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