Boaz Ilan, Department of Applied Mathematics, University of California Merced

Dry dam break, rarefaction waves, and white holes

When a reservoir's fluid is suddenly released onto a dry bed, a rarefaction wave arises. We study this for a superfluid Bose-Einstein condensate (BEC) confined in a harmonic trap, which is modeled by a Gross-Pitaevskii / Nonlinear Schrödinger (GP / NLS) equation. A generalized rarefaction wave ensues, for which both Riemann invariants are varying. A self-similar solution of the second kind provides insight into this dynamics, leading to white hole analogues and a gradient catastrophe. The analytical results agree with simulations and BEC experiments.