The phenomenon of revivals on complex potential Schrödinger’s equation

  • Lyonell Boulton

    Heriot-Watt University, Edinburgh, UK
  • George Farmakis

    Heriot-Watt University, Edinburgh, UK; London South Bank University, London, UK
  • Beatrice Pelloni

    Heriot-Watt University, Edinburgh, UK
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Abstract

The mysterious phenomenon of revivals in linear dispersive periodic equations was discovered first experimentally in optics in the 19th century, then rediscovered several times by theoretical and experimental investigations. While the term has been used systematically and consistently by many authors, there is no consensus on a rigorous definition. In this paper, we describe revivals modulo a regularity condition in a large class of Schrödinger’s equations with complex bounded potentials. As we show, at rational times, the solution is given explicitly by finite linear combinations of translations and dilations of the initial datum, plus an additional continuous term.

Cite this article

Lyonell Boulton, George Farmakis, Beatrice Pelloni, The phenomenon of revivals on complex potential Schrödinger’s equation. Z. Anal. Anwend. 43 (2024), no. 3/4, pp. 401–416

DOI 10.4171/ZAA/1762