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Nonlinear wave propagation governed by a fractional derivative
Van Thuy Hoang1,2, Justin Widjaja3,4,5, Y Long Qiang3,4
1Institute of Photonics and Optical Science (IPOS), School of Physics A28, The University of Sydney, Sydney, New South Wales, Australia. vanthuy.hoang@sydney.edu.au.
Nature Communications
|July 2, 2025
Summary
Researchers report the first experimental observation of temporal solitons governed by fractional nonlinear wave equations. These solitons exhibit non-exponential tails, highlighting their nonlocal nature and a small time-bandwidth product.
Area of Science:
- Nonlinear physics
- Wave phenomena
- Fractional calculus
Background:
- Fractional derivatives have a long history and applications in physics, particularly in systems with nonlocal interactions.
- Experimental studies of fractional systems are rare due to implementation challenges.
Purpose of the Study:
- To experimentally observe and characterize temporal solitons governed by a fractional nonlinear wave equation.
- To investigate the unique properties of these solitons, such as their tail behavior and time-bandwidth product.
Main Methods:
- Observation and characterization of temporal solitons.
- Utilizing a fractional nonlinear wave equation to describe soliton behavior.
Main Results:
- Successfully observed and fully characterized a family of temporal solitons.
- Demonstrated that these solitons possess non-exponential tails, indicative of their nonlocal characteristics.
- Measured a very small time-bandwidth product for the observed solitons.
Conclusions:
- The experimental realization of fractional solitons opens new avenues for studying nonlocal phenomena in physics.
- The observed non-exponential tails and small time-bandwidth product provide unique insights into the behavior of fractional systems.
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