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Exploding dissipative solitons in reaction-diffusion systems.

Orazio Descalzi1, Nail Akhmediev, Helmut R Brand

  • 1Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago, Chile and Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany.

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Summary
This summary is machine-generated.

Exploding dissipative solitons emerge in reaction-diffusion systems, transitioning through oscillatory and meandering states. These solitons propagate unidirectionally, a behavior unique to lower-symmetry systems like the one studied.

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Area of Science:

  • Nonlinear dynamics
  • Chemical kinetics
  • Mathematical physics

Background:

  • Dissipative solitons are localized waves in open systems.
  • Exploding dissipative solitons are known in the cubic-quintic complex Ginzburg-Landau (CGL) equation.
  • Understanding soliton dynamics in different systems is crucial.

Purpose of the Study:

  • To investigate the emergence and behavior of exploding dissipative solitons in a reaction-diffusion system.
  • To explore the parameter space and transitions between different soliton states.
  • To compare the findings with existing models like the CGL equation.

Main Methods:

  • Numerical simulations of a reaction-diffusion model.
  • Analysis of system dynamics as a function of a vorticity parameter.
  • Observation and characterization of localized states and their transitions.

Main Results:

  • Exploding dissipative solitons were observed in the reaction-diffusion system.
  • A sequence of transitions was identified: oscillatory localized states, meandering dissipative solitons, and exploding dissipative solitons.
  • Unidirectional propagation of exploding dissipative solitons was demonstrated.
  • A reverse cascade back to oscillatory states was observed.

Conclusions:

  • Reaction-diffusion systems can exhibit exploding dissipative solitons.
  • The observed unidirectional propagation of exploding solitons requires lower system symmetry.
  • This study expands the understanding of soliton dynamics beyond the CGL equation.