Analysis of interaction dynamics and rogue wave localization in modulation instability using data-driven dominant...

Area of Science:

• Nonlinear optics
• Data-driven science
• Computational physics

Background:

• Modulation instability (MI) in nonlinear systems, such as optical fibers, is crucial for understanding wave propagation.
• Identifying dominant physical processes governing MI typically relies on expert intuition and asymptotic analysis.
• Existing methods struggle to automatically differentiate complex interaction regimes within chaotic dynamics.

Purpose of the Study:

• To develop and apply a machine learning technique, data-driven dominant balance, for automated analysis of MI dynamics.
• To distinguish between nonlinear propagation and nonlinearity-dispersion driven localization in various MI regimes.
• To extend the automated analysis to complex, noise-driven spontaneous MI and chaotic propagation.

Main Methods:

• Application of data-driven dominant balance, a machine learning approach, to analyze the nonlinear Schrödinger equation.
• Interpretation of established analytical solutions for Akhmediev breather, Kuznetsov-Ma, and Peregrine soliton (rogue wave) structures.
• Numerical simulations of noise-driven spontaneous modulation instability to test the method's robustness.

Main Results:

• Successfully automated the identification of dominant physical processes governing MI.
• Distinguished regions of dominant nonlinear propagation from those driven by combined nonlinearity and dispersion.
• Isolated distinct regimes of dominant physical interactions in spontaneous MI and chaotic propagation dynamics.

Conclusions:

• Data-driven dominant balance offers an effective, automated approach to analyzing complex nonlinear dynamics.
• The method provides new insights into distinguishing physical drivers in different MI regimes.
• This technique holds promise for advancing the study of wave propagation in nonlinear systems.