Nonlinear wave propagation governed by a fractional derivative
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Date
2025
Authors
Hoang, V.T.
Widjaja, J.
Qiang, Y.L.
Liu, M.K.
Alexander, T.J.
Runge, A.F.J.
de Sterke, C.M.
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Journal article
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Nature Communications, 2025; 16(1):5469-1-5469-8
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Van Thuy Hoang, Justin Widjaja, Y. Long Qiang, Maxwell K. Liu, Tristram J. Alexander, Antoine F. J. Runge, C. Martijn de Sterke
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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.
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© The Author(s) 2025. Open Access. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived fromthis article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creativecommons.org/licenses/by-nc-nd/4.0/.