Breakdown of waves described by exact solutions of the Thomas-Fermi model

The dynamics of large localized repulsive clouds is examined by means of exact non-stationary solutions of the one-dimensional Thomas-Fermi model. The nonlinear flattening of the cloud peak, the wave breakdown at the cloud peripheries, and the condensate velocity distributions are thus described. Our solutions, which can contain an arbitrary amount of free parameters, show the nonlinear evolution of an arbitrary initial wave form. A unique procedure for analyzing these solutions is presented. The difference between our breakdown matter wave solutions and the well known Riemann shock waves is stressed.