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SUMMARY:Wave patterns beneath an ice cover - Andrej Il’ichev (Steklov Ma
 thematical Institute\, Russian Academy of Sciences )
DTSTART:20171003T151500Z
DTEND:20171003T160000Z
UID:TALK87411@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We prove existence of the soliton-like solutions of the full s
 ystem of equations which describe wave propagation in the fluid of a finit
 e depth under an ice cover. These solutions correspond to solitary waves o
 f various nature propagating along the water-ice interface. We consider th
 e plane-parallel movement in a layer of the perfect fluid of the finite de
 pth which characteristics obey the full 2D Euler system of equations. The 
 ice cover is modeled by the elastic Kirchgoff-Love plate and it has a cons
 iderable thickness so that the plate inertia is taken into consideration w
 hen the model is formulated. The Euler equations contain the additional pr
 essure arising from the presence of the elastic plate freely floating on t
 he liquid surface. The mentioned families of the solitary waves are parame
 terized by a speed of the wave and their existence is proved for the speed
 s lying in some neighborhood of its critical value corresponding to the qu
 iescent state. S olitary waves\, in their turn\, bifurcate from the quiesc
 ent state and lie in some neighborhood of it. By other words\, existence o
 f solitary waves of sufficiently small amplitudes on the water-ice interfa
 ce is proved. The proof is conducted with the help of the projection of th
 e required system to the central manifold and further analysis of the resu
 lting reduced finite dimensional dynamical system on the central manifold.
LOCATION:Seminar Room 1\, Newton Institute
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