Talbot effect for the cubic nonlinear Schrödinger equation on the torus

2013/03/14 by M. Burak Erdoğan, Erdogan, M. B., Nikolaos Tzirakis +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1303.3604

openalex publication_date 2013/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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