TY - JOUR

T1 - Bound pairs of fronts in a real Ginzburg-Landau equation coupled to a mean field

AU - Herrero, Henar

AU - Riecke, Hermann

N1 - Funding Information:
This work was supportedb y DOE throughg rant (DE-FG02-92ER14303a)n d by an equipmengtr ant from NSF (DMS-9304397)H. .H. was supportebdy a grant of the EP.I. programR ef. AP90 09297081 (M.E.C.). H.R. thanksth eU niversidadde N avarrafo r its hospitalityW. e gratefullay cknowledghee lpfuls ug-gestionbs y W.U Kath and discussionws ithV. Hakim and with P. Kolodnerw, hokindly sharedh is dataw ith us prior to publication.

PY - 1995/7/15

Y1 - 1995/7/15

N2 - 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.

AB - 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.

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U2 - 10.1016/0167-2789(95)00068-F

DO - 10.1016/0167-2789(95)00068-F

M3 - Article

AN - SCOPUS:0003026071

VL - 85

SP - 79

EP - 92

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -