The dynamics of matter waves in two-dimensional, magnetically trapped Bose-Einstein
condensates are of great interest both mathematically and physically. I will outline the physical problem, show some of the structures that have been observed numerically, analytically, and experimentally, and then give an idea as to what type of analysis can be done on the problem. The analysis will primarily focus upon the existence and spectral stability of matter waves which arise as steady-state solutions in a rotating frame.
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