Crossover dynamics of dispersive shocks in Bose-Einstein condensates characterized by two and three-body interactions

We show that the perturbative nonlinearity associated with three-atom interactions, competing with standard two-body repulsive interactions, can change dramatically the evolution of 1D dispersive shock waves in a Bose-Einstein condensate. In particular, we prove the existence of a rich crossover dynamics, ranging from the formation of multiple shocks regularized by coexisting trains of dark and antidark matter waves, to 1D soliton collapse. For a given scattering length, all these different regimes can be accessed by varying the number of atoms in the condensate.