We observe the formation of shock waves in a Bose-Einstein condensate containing a large number of sodium atoms. The shock wave is initiated with a repulsive blue-detuned light barrier, intersecting the BoseEinstein condensate, after which two shock fronts appear. We observe breaking of these waves when the size of these waves approaches the healing length of the condensate. At this time, the w...

It has been observed by various authors [3, 4, 5, 6, 8, 12] that the Riemann problem for certain equations from nonlinear elasticity and gasdynamics cannot be solved for all combinations of piecewise constant initial states with shock waves, rarefaction waves and contact discontinuities only. For that reason, the notion of a delta shock wave and a singular shock wave was introduced and employed...

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing...