We study the evolution of the one dimensional periodic cubic Schrödinger equation (NLS) with bounded variation data. For the linear evolution, it is known that for irrational times the solution is a continuous, nowhere differentiable fractal-like curve. For rational times the solution is a linear combination of finitely many translates of the initial data. Such a dichotomy was first observed by Talbot in an optical experiment performed in 1836, . In this paper, we prove that a similar phenomenon occurs in the case of the NLS equation.
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