Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation.

Abstract

We study the wave breaking mechanism for the weakly dispersive defocusing nonlinear Schrödinger equation with a constant phase dark initial datum that contains a vacuum point at the origin. We prove by means of the exact solution to the initial value problem that, in the dispersionless limit, the vacuum point is preserved by the dynamics until breaking… (More)

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