Etude de solitons en théorie classique des champs de basse dimension

Abstract : This thesis focuses on the analysis of some Chern-Simons models in 2D 1. Part 1: from the Painleve test, we determine sufficient conditions for integrability static model Jackiw-Pi. The unique integrated resulting reduction is self-dual reduction. We also establish a Bäcklund transformation that gives the solutions of the Liouville equation. We show, with assumptions of regularity and decay spatial infinity, the solutions that represent non-topological vortex depend on a rational function of complex variable. Solutions representative n-vortex thus form a space 4n dimensions. Part 2: we find self-dual solutions electrically charged for the model of Manton. These solutions represent topological vortex. We interpret this model as a Chern-Simons system in an external electromagnetic field. With this understanding, we build, in addition to geometric symmetries, hidden symmetries of the model; there is a five parameters group of hidden symmetries. We give a relativistic generalization of Manton model. It admits a self-dual reduction whose non-relativistic limit is the self-dual Manton reduction. Finally, we propose a model for one-half spin particles. This system generalizes Manton model and Duval-Horvathy-Palla model. Partie-3: we propose a generalization of Girvin-McDonnald model for quantum Hall effect. It admits, according to the ground state, topological vortex finite energy and non-topological vortex infinite energy. To understand this particular case, we show that it is the limit of two models, one with topological vortex, the other with non-topological vortex. We also show that it is a special case of Manton model.
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Yera Niangoura. Etude de solitons en théorie classique des champs de basse dimension. Mathématiques [math]. Université de Tours, 1998. Français. ⟨tel-01270457⟩

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