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State transition induced by higher-order effects and background frequency.

Chong Liu1, Zhan-Ying Yang1, Li-Chen Zhao1

  • 1School of Physics, Northwest University, Xi'an 710069, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

This study explores the transition between Peregrine rogue waves and W-shaped waves, revealing a connection to modulation instability (MI). The findings link MI growth rates to wave localization, offering insights into nonlinear wave dynamics.

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Area of Science:

  • Nonlinear wave dynamics
  • Mathematical physics
  • Fluid mechanics

Background:

  • Peregrine rogue waves and W-shaped traveling waves are complex nonlinear phenomena.
  • Understanding state transitions between these wave types is crucial for predicting their behavior.
  • Higher-order effects and background frequency significantly influence wave dynamics.

Purpose of the Study:

  • To investigate the state transition between Peregrine rogue waves and W-shaped traveling waves.
  • To analyze the role of higher-order effects and background frequency in this transition.
  • To explore the relationship between modulation instability (MI) and wave transition characteristics.

Main Methods:

  • Utilizing an exact explicit rational solution to describe the wave transition.
  • Applying modulation instability (MI) analysis to identify stable and unstable regions.
  • Deriving analytical relationships between MI growth rate and transition characteristics.

Main Results:

  • The transition is consistent with modulation instability (MI) analysis, showing distinct MI and stability regions.
  • A direct analytical link is established between the MI growth rate and the localization characteristic of the transition.
  • The interaction of second-order waves in the stability region results in a line structure, differing from elastic interactions.

Conclusions:

  • Higher-order effects and background frequency drive the transition between Peregrine rogue and W-shaped waves.
  • Modulation instability analysis provides a framework for understanding this transition.
  • The study offers a deeper understanding of nonlinear wave interactions and their unique structural outcomes.