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<p>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.</p>

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Nonlinear wave propagation governed by a fractional derivative

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月1日

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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

摘要

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.