Nonlinear wave propagation governed by a fractional derivative

Hoang Van Thuy (), Justin Widjaja, Y. Long Qiang, Maxwell K. Liu, Tristram J. Alexander, Antoine F. J. Runge and C. Martijn Sterke
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Hoang Van Thuy: The University of Sydney
Justin Widjaja: The University of Sydney
Y. Long Qiang: The University of Sydney
Maxwell K. Liu: The University of Sydney
Tristram J. Alexander: The University of Sydney
Antoine F. J. Runge: The University of Sydney
C. Martijn Sterke: The University of Sydney

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally in systems with nonlocal temporal or spatial interactions. However, systematic experiments have been rare because the physical implementation is challenging. Here we report the observation and full characterization of a family of temporal solitons that are governed by a fractional nonlinear wave equation. We demonstrate that these solitons have non-exponential tails, reflecting their nonlocal character, and have a very small time-bandwidth product.

Date: 2025
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DOI: 10.1038/s41467-025-60625-4

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