Properties of the Hilbert–Nonlinear Schrödinger Solitons and Related Nonlocal Systems
Creators
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1.
University of Sydney
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2.
California Institute of Technology
Abstract
We present a theoretical and experimental study of Hilbert–nonlinear Schrödinger solitons, which occur in the presence of dispersion described by a fractional Laplacian. This leads to soliton solutions that differ significantly from those associated with dispersion relations represented by integer derivatives. We investigate the fundamental properties of the governing equation and find approximate solutions using both a variational method and a projection-based approach. Our analysis is extended to an experimental and theoretical investigation of a related system that combines fractional and quadratic dispersion, for which we report distinct types of solitons.
Copyright and License
© 2025, American Chemical Society
Supplemental Material
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.5c01158.
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Description of the mode-locked laser used in the experiments and the technique employed to measure and characterize the pulses (PDF)
Funding
This research was supported by the Australian Research Council Centre of Excellence in Optical Microcombs for breakthrough Science (project number CE230100006), and by the Australian Research Council projects DE220100509, DP230102200.
Files
hoang-et-al-2025-properties-of-the-hilbert-nonlinear-schrödinger-solitons-and-related-nonlocal-systems.pdf
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Additional details
Funding
- Australian Research Council
- Centre of Excellence in Optical Microcombs CE230100006
- Australian Research Council
- DE220100509
- Australian Research Council
- DP230102200