This week's Mathematical Sciences Department colloquium is given by Dr. Yannan Shen, Research Associate, Mathematical Sciences Department of The University of Texas at Dallas.
We consider ultra-short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. We will derive short-pulse equation (SPE) in frequency band gaps. We will discuss SPE in its characteristic coordinate and the transformation to sine-Gordon equation, and robustness of various solutions emanating from the sine-Gordon equation and their periodic generalizations. We will discuss the connection of (regularized) SPE with the nonlinear Schrodinger equation. Finally we will discuss the wellposedness of generalized Ostrovsky equation with small initial data.
Coffee will be served in FO 2.610F at 1:30 PM.
***PLEASE NOTE THAT TODAY'S COLLOQUIUM HAS BEEN MOVED TO A DIFFERENT LOCATION***
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