Bound pairs of fronts in a real Ginzburg-Landau equation coupled to a mean field

Henar Herrero*, Hermann Riecke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Motivated by the observation of localized traveling-wave states ('pulses') convection in binary liquid mixtures, the interaction of fronts is investigated in a real Ginzburg-Landau equation which is coupled to a mean field. In that system the Ginzburg-Landau equation describes the traveling-wave amplitude and the mean field corresponds to a concentration mode which arises due to the slowness of mass diffusion. It is shown that for single fronts the mean field can lead to a hysteretic transition between slow and fast fronts. Its contribution to the interaction between fronts can be attractive as well as repulsive and depends strongly on their direction of propagation. Thus, the concentration mode leads to a new localization mechanism, which does not require any dispersion in contrast to that operating in the nonlinear Schrödinger equation. Based on this mechanism alone, pairs of fronts in binary-mixture convection are expected to form stable pulses if they travel backward, i.e. opposite to the phase velocity. For positive velocities the interaction becomes attractive and destabilizes the pulses. These results are in qualitative agreement with recent experiments. Since the new mechanism is very robust it is expected to be relevant in other systems as well in which a wave is coupled to a mean field.

Original languageEnglish (US)
Pages (from-to)79-92
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - Jul 15 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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