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Front propagation in weakly subcritical pattern-forming systems.

Benjamin C Ponedel1, Hsien-Ching Kao2, Edgar Knobloch1

  • 1Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.

Physical Review. E
|January 20, 2018
PubMed
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This study examines front dynamics in the bistable Ginzburg-Landau equation, revealing how stable solutions may not always emerge from initial conditions, leading to complex behaviors.

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Chemical kinetics

Background:

  • Front propagation is crucial in various scientific fields.
  • Understanding transitions between different front behaviors is key.
  • The bistable Ginzburg-Landau equation models complex pattern formation.

Purpose of the Study:

  • Investigate front speed and stability near a steady-state bifurcation.
  • Analyze the transition between pushed and pulled fronts.
  • Explore the selection mechanisms for front solutions.

Main Methods:

  • Construct exact nonlinear front solutions.
  • Analyze the stability of these exact solutions.
  • Employ numerical techniques to study chaotic dynamics.

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Main Results:

  • Identified cases where exact solutions are stable but not selected.
  • Observed instances where exact solutions are unstable, leading to distinct front selection.
  • Demonstrated the emergence of chaotic front dynamics.

Conclusions:

  • Front selection is sensitive to initial conditions and stability properties.
  • The bistable Ginzburg-Landau equation exhibits rich dynamics, including chaos.
  • Exact solutions provide insights but do not fully capture all emergent behaviors.