dorsal/arxiv
View SchemaBound Pairs of Fronts in a Real Ginzburg-Landau Equation Coupled to a Mean Field
| Authors | Henar Herrero, Hermann Riecke |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9409001 |
| URL | https://arxiv.org/abs/patt-sol/9409001 |
| DOI | 10.1016/0167-2789(95)00068-F |
| Journal | Physica D 85 (1995) 79-92 |
Abstract
Motivated by the observation of localized traveling-wave states (`pulses') in 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 corrsponds to a concentration mode which arises due to the slowness of mass diffusion. 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 Schr\"odinger equation. Based on this mechanism alone, pairs of fronts in binary-mixture convection are expected to form {\it stable} pulses if they travel {\it 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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"abstract": "Motivated by the observation of localized traveling-wave states (`pulses\u0027) in\nconvection in binary liquid mixtures, the interaction of fronts is investigated\nin a real Ginzburg-Landau equation which is coupled to a mean field. In that\nsystem the Ginzburg-Landau equation describes the traveling-wave amplitude and\nthe mean field corrsponds to a concentration mode which arises due to the\nslowness of mass diffusion. For single fronts the mean field can lead to a\nhysteretic transition between slow and fast fronts. Its contribution to the\ninteraction between fronts can be attractive as well as repulsive and depends\nstrongly on their direction of propagation. Thus, the concentration mode leads\nto a new localization mechanism, which does not require any dispersion in\ncontrast to that operating in the nonlinear Schr\\\"odinger equation. Based on\nthis mechanism alone, pairs of fronts in binary-mixture convection are expected\nto form {\\it stable} pulses if they travel {\\it backward}, i.e. opposite to the\nphase velocity. For positive velocities the interaction becomes attractive and\ndestabilizes the pulses. These results are in qualitative agreement with recent\nexperiments. Since the new mechanism is very robust it is expected to be\nrelevant in other systems as well in which a wave is coupled to a mean field.",
"arxiv_id": "patt-sol/9409001",
"authors": [
"Henar Herrero",
"Hermann Riecke"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/0167-2789(95)00068-F",
"journal_ref": "Physica D 85 (1995) 79-92",
"title": "Bound Pairs of Fronts in a Real Ginzburg-Landau Equation Coupled to a Mean Field",
"url": "https://arxiv.org/abs/patt-sol/9409001"
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