Collision of rarefaction waves in Bose-Einstein condensates

We consider the problem of expansion of Bose-Einstein condensate released form a box. On the contrary to the standard situation of release from a harmonic trap, in this case the dynamics is complicated by a process of collision of two rarefaction waves propagating to the center of the initially uniform distribution. Complete analytical solution of this problem is obtained by Riemann method in hydrodynamic dispersionless approximation and the results are compared with the exact numerical solution of the Gross-Pitaevskii equation.