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Modified linear stability analysis for quantitative dynamics of a perturbed plane wave.

Peng Gao1,2, Chong Liu1,2, Li-Chen Zhao1,2

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

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We developed a new method to predict how perturbed plane waves behave in nonlinear systems. This approach accurately forecasts wave dynamics and improves upon existing linear stability analysis (LSA) techniques.

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Area of Science:

  • Nonlinear optics
  • Wave propagation dynamics
  • Computational physics

Background:

  • Plane waves in nonlinear systems are fundamental but their perturbed dynamics are complex.
  • Existing linear stability analysis (LSA) methods have limitations in predicting these dynamics accurately.
  • Understanding perturbed wave behavior is crucial for applications in fiber optics and other nonlinear media.

Purpose of the Study:

  • To develop and validate a quantitative method for predicting the dynamics of perturbed plane waves in nonlinear systems.
  • To demonstrate the effectiveness of the developed method using a nonintegrable fiber model with fourth-order dispersion.
  • To investigate the differences in perturbation growth between localized and periodic disturbances.

Main Methods:

  • Linear stability analysis (LSA) was adapted and extended for quantitative prediction.
  • A nonintegrable fiber model with fourth-order dispersion was used as a test case.
  • Gaussian-type initial perturbations with cosine-type modulations were analyzed.

Main Results:

  • The method successfully predicted propagation velocities, periodicity, and localization of perturbed plane waves.
  • The range of applicability for the developed LSA method was discussed.
  • Modulation-instability-induced growth of localized perturbations was shown to differ from purely periodic perturbations, requiring modified gain values for accurate prediction.

Conclusions:

  • The enhanced LSA method provides a significant improvement for predicting perturbed plane wave dynamics.
  • The study highlights the need for modified gain values when analyzing localized perturbations in nonlinear systems.
  • This work offers a valuable tool for studying complex wave phenomena in practical nonlinear systems.