Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts generating Periodic or Chaotic States

Details Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts generating Periodic or Chaotic States Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts generating Periodic or Chaotic States

1999-08-16

arxiv.org/abs/patt-sol/9908007v1

Phys. Rev. E 61, R6063-6066 (2000)

Physics

Condensed Matter

4 pages Revtex, 2 figures, submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevE.61.R6063

We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state. The ``leading edge representation'' of the equation of motion reveals the universal nature of their propagation mechanism and allows us to generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts, that generate periodic or even chaotic states. Such fronts in addition exhibit a universal algebraic phase relaxation. We numerically verify our analytical predictions for the Swift-Hohenberg and the Complex Ginzburg Landau equation.

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