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Strongly asymmetric soliton explosions.

Nail Akhmediev1, J M Soto-Crespo

  • 1Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
PubMed
Summary

Dissipative systems exhibit asymmetric soliton explosions, alternating sides despite symmetric conditions. This phenomenon is explained by linear stability analysis and a three-stage cooling process.

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Area of Science:

  • Nonlinear dynamics
  • Soliton physics
  • Complex systems

Background:

  • Dissipative systems can exhibit complex behaviors.
  • Solitons are stable, self-reinforcing wave packets.
  • The complex cubic-quintic Ginzburg-Landau equation models various nonlinear phenomena.

Purpose of the Study:

  • To investigate asymmetric soliton explosions in dissipative systems.
  • To understand the underlying mechanisms of these explosions.
  • To analyze the transition from stationary to exploding solitons.

Main Methods:

  • Numerical simulations of the one-dimensional complex cubic-quintic Ginzburg-Landau equation.
  • Linear stability analysis of unstable solitons.
  • Observation and description of the soliton explosion process.

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Main Results:

  • Observed strongly asymmetric soliton explosions in numerical simulations.
  • Explosions occurred on alternating sides of the soliton, despite symmetric initial conditions and equations.
  • Identified a three-stage process of soliton cooling during the transition to explosion.

Conclusions:

  • Asymmetric soliton explosions in dissipative systems are a robust phenomenon.
  • Linear stability analysis provides insight into the alternating explosion sides.
  • Soliton cooling is a key aspect of the transition to explosive dynamics.