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

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