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The Cauchy problem for μHS equation: Weak solutions and integrability

Infinite-Dimensional Geometry December 07, 2013 - December 08, 2013

December 07, 2013 (03:00 PM PST - 03:35 PM PST)
Speaker(s): Feride Tiglay (Ohio State University)
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Abstract μHS equation has a physical interpretation in the context of liquid crystals and is derived as an Euler-Arnold equation on the group of circle diffeomorphisms. Like its ''cousins'' in this framework, it has certain manifestations of integrability---a Lax pair, a bi-Hamiltonian structure and peakon solutions. I will briefly discuss existence of weak solutions and a way of constructing special functions to integrate the equation.
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