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Existence of excited states for a nonlinear Dirac field |
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| Authors: | Mikhael Balabane Thierry Cazenave Adrien Douady Frank Merle |
| Affiliation: | 1. CSP, Université Paris-Nord, Avenue J. B. Clément, F-93430, Villetanneuse, France 2. CMA, Ecole Normale Supérieure, 45, rue d'Ulm, F-75230, Paris Cedex 05, France 3. Analyse Numérique, Université Pierre et Marie Curie, 4, place Jussieu, F-75252, Paris Cedex 05, France 4. Département de Mathématiques, Université Paris-Sud, F-91405, Orsay Cedex, France 5. Ecole Normale Supérieure, 45, rue d'Ulm, F-75230, Paris Cedex 05, France |
| Abstract: | We prove the existence of infinitely many stationary states for the following nonlinear Dirac equation $$igamma ^mu partial _mu psi - mpsi + (bar psi psi )psi = 0.$$ Seeking for eigenfunctions splitted in spherical coordinates leads us to analyze a nonautonomous dynamical system inR 2. The number of eigenfunctions is given by the number of intersections of the stable manifold of the origin with the curve of admissible datum. This proves the existence of infinitely many stationary states, ordered by the number of nodes of each component. |
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