Mark Hoefer Department of Applied Mathematics, University of Colarado at Boulder Dispersive shock waves in a Bose-Einstein Condensate Wednesday 7th September 14:05-14:55pm, Carslaw Building Room 373. A Bose-Einstein condensate (BEC) is a quantum fluid that can give  rise to interesting nonlinear dynamics.  Recent experiments by Eric  Cornell's BEC group at JILA, University of Colorado at Boulder,  showcase a BEC that exhibits behavior apparently similar to that of a  shock wave in a compressible gas, eg.  traveling fronts with steep  gradients. However, the governing Gross-Pitaevskii (GP) equation that  describes the mean field of a BEC admits no dissipation hence, based  on this theory, classical shock solutions should not exist.  Instead,  gas dynamics with small, positive dispersion is considered and it is  shown that weak dispersion is a mechanism for the generation of a  novel kind of shock wave.  Computations with the GP equation are  compared to those from dissipative gas dynamics and to direct  experiment.  The analytical structure of the canonical 1D dispersive  shock problem is explained.  The results indicate that these steep  gradients correspond to dispersive shock waves and that the sharp  fronts can be viewed as slowly modulated trains of gray solitons.   Fundamental differences between the dynamics of dispersive shocks and  classical shocks, such as shock speed and shock interaction are  elucidated.