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We study the wave breaking mechanism for the weakly dispersive defocusingnonlinear Schroedinger (NLS) equation with a constant phase dark initial datumthat contains a vacuum point at the origin. We prove by means of the exactsolution to the initial value problem that, in the dispersionless limit, thevacuum point is preserved by the dynamics until breaking occurs at a finitecritical time. In particular, both Riemann invariants experience a simultaneousbreaking at the origin. Although the initial vacuum point is no longerpreserved in the presence of a finite dispersion, the critical behaviourmanifests itself through an abrupt transition occurring around the breakingtime.

Breaking mechanism from a vacuum point in the defocusing nonlinear Schroedinger equation