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We study the evolution of the one dimensional periodic cubic Schr\"odingerequation (NLS) with bounded variation data. For the linear evolution, it isknown that for irrational times the solution is a continuous, nowheredifferentiable fractal-like curve. For rational times the solution is a linearcombination of finitely many translates of the initial data. Such a dichotomywas first observed by Talbot in an optical experiment performed in 1836. Inthis paper we prove that a similar phenomenon occurs in the case of the NLSequation.

Talbot effect for the cubic nonlinear Schr\"odinger equation on the torus