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Diverging probability-density functions for flat-top solitary waves.

Avner Peleg1, Yeojin Chung, Tomás Dohnal

  • 1Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

Disorder in nonlinear gain affects solitary waves. The probability of wave amplitude follows a loglognormal distribution near its maximum, similar to previous findings with linear gain.

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Area of Science:

  • Nonlinear optics
  • Statistical physics

Background:

  • Solitary waves are fundamental in nonlinear systems.
  • Disorder can significantly alter wave propagation statistics.

Purpose of the Study:

  • Investigate the statistical properties of flat-top solitary waves under dissipative disorder.
  • Analyze the impact of cubic nonlinear gain disorder on solitary wave amplitude.

Main Methods:

  • Perturbative analytic calculations.
  • Monte Carlo simulations.
  • Analysis of the cubic-quintic nonlinear Schrödinger equation (CQNLSE).

Main Results:

  • Probability-density function (PDF) of amplitude exhibits loglognormal divergence near maximum amplitude.
  • This behavior mirrors findings for linear gain disorder.
  • PDF of a combined amplitude-velocity parameter also shows loglognormal divergence.

Conclusions:

  • Disorder in nonlinear gain leads to predictable statistical behaviors in solitary waves.
  • Loglognormal divergence is a robust feature across different types of gain disorder.