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SUMMARY:The Hunter-Saxton system: more than a generalization
DTSTART:20130318T171500
DTEND:20130318T180000
DTSTAMP:20260510T105754Z
UID:48993acc732fa25207aaf68320d6901bfe52e7cac3b0d2acc74be6dc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Marcus Wunsch\, ETH Zürich\nHamiltonian Dynamics Seminar\nAbs
 tract: In this talk\, I will review some recent work on the Hunter-Saxton 
 system\, subject to periodic boundary conditions. The Hunter-Saxton system
  is a generalization of the (single-component) Hunter-Saxton equation\, wh
 ich describes the propagation of weakly nonlinear orientation waves in a m
 assive director field of a nematic liquid crystal. Moreover\, the system (
 1) is the high-frequency limit of the two-component Camassa-Holm equation 
 arising in the theory of shallow water waves\, and it has also been propos
 ed as a model for the nonlinear dynamics of dark matter. After preparing t
 he analytic foundations for this coupled nonlinear system\, I will prove t
 hat classical solutions to (1) have explicit representations in terms of t
 heir Lagrangian coordinates. The latter\, it turns out\, describe the geod
 esics on an infinite-dimensional sphere (κ = 1) or pseudosphere (κ = −
 1)\, which a posteriori reveals why there are explicit solution formulae. 
 Finally\, I will show how the geometric picture guides us naturally to the
  construction of weak solutions.
LOCATION:MA A3 30 http://plan.epfl.ch/?room=MA%20A3%2030
STATUS:CONFIRMED
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