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, [20]. In this paper, we prove that a similar phenomenon occurs in the case of the NLS equation. © International Press 2013.
CITATION STYLE
Erdoǧan, M. B., & Tzirakis, N. (2013). Talbot effect for the cubic non-linear schrödinger equation on the torus. Mathematical Research Letters, 20(6), 1081–1090. https://doi.org/10.4310/MRL.2013.v20.n6.a7
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