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Nonlinear wave propagation governed by a fractional derivative

Author

Listed:
  • Van Thuy Hoang

    (The University of Sydney
    ARC Centre of Excellence for Optical Microcombs for Breakthrough Science (COMBS))

  • Justin Widjaja

    (The University of Sydney
    ARC Centre of Excellence for Optical Microcombs for Breakthrough Science (COMBS)
    California Institute of Technology)

  • Y. Long Qiang

    (The University of Sydney
    ARC Centre of Excellence for Optical Microcombs for Breakthrough Science (COMBS))

  • Maxwell K. Liu

    (The University of Sydney)

  • Tristram J. Alexander

    (The University of Sydney)

  • Antoine F. J. Runge

    (The University of Sydney
    ARC Centre of Excellence for Optical Microcombs for Breakthrough Science (COMBS))

  • C. Martijn Sterke

    (The University of Sydney
    ARC Centre of Excellence for Optical Microcombs for Breakthrough Science (COMBS))

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.

Suggested Citation

  • Van Thuy Hoang & Justin Widjaja & Y. Long Qiang & Maxwell K. Liu & Tristram J. Alexander & Antoine F. J. Runge & C. Martijn Sterke, 2025. "Nonlinear wave propagation governed by a fractional derivative," Nature Communications, Nature, vol. 16(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-60625-4
    DOI: 10.1038/s41467-025-60625-4
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