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Updated: Apr 29, 2026
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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
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Many-body interaction in fast soliton collisions.
Avner Peleg1, Quan M Nguyen2, Paul Glenn1
1Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA.
Summary
High-order pulse interactions significantly impact nonlinear Schrödinger (NLS) soliton collisions with weak nonlinear loss. These complex dynamics, dependent on initial positions, differ from standard cubic loss scenarios.
Area of Science:
- Nonlinear dynamics
- Soliton interactions
- Mathematical physics
Background:
- Cubic nonlinear Schrödinger (NLS) equation governs many physical phenomena.
- Soliton collisions are crucial for understanding wave packet behavior.
- Nonlinear loss complicates soliton dynamics.
Purpose of the Study:
- To investigate n-pulse interactions in fast NLS soliton collisions.
- To analyze the effect of generic weak nonlinear loss on soliton amplitude shifts.
- To develop a generalized model for predicting these interactions.
Main Methods:
- Development of a generalized reduced model for n-pulse interactions.
- Numerical solutions of the perturbed NLS equation.
- Analysis of collisions with septic loss (m=3) and generic nonlinear loss (mc=3).
Main Results:
- Three-pulse interaction dominates amplitude shifts even in four-soliton collisions.
- Amplitude shifts are highly sensitive to initial soliton positions.
- High-order pulse interactions are key in generic nonlinear loss scenarios.
Conclusions:
- n-pulse interactions play a critical role in fast NLS soliton collisions with weak nonlinear loss.
- Collision dynamics become complex and deviate from cubic loss behavior.
- The developed model quantitatively demonstrates these effects.
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