Supersonic Dispersive Fluid Dynamics

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This project examines supersonic flows in dispersive fluids experiencing negligible dissipative effects. The main objective is to develop an understanding of fundamental excitations in dispersive fluids which are physically relevant for a number of systems including Bose-Einstein condensates, optics, plasma, and shallow water. Such excitations include oblique dispersive shock waves which will be constructed for a number of nonlinear dispersive wave equations. Properties, including stability and the behavior of interacting dispersive shock waves, will be investigated and applied to the study of multidimensional boundary value problems.Thunder, the crack of a whip, and the boom heard from a jet plane surpassing the speed of sound are familiar occurrences in human experience and all result from the generation of viscous shock waves. This project will focus on a very different type of shock wave that propagates through dispersive media such as the superfluidic Bose-Einstein condensate (BEC), nonlinear photonic crystals, plasma, and shallow water. Applications of this theory include the control of nonlinear waves, fostering advances in modern technologies such as matter lasers, atomic interferometry, and imaging.