Remarques sur les mesures de Wigner |
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| Institution: | 1. Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei, MG 36307-352, Brazil;2. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, Maribor SI-2000, Slovenia;3. CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, Maribor SI-2000, Slovenia;4. Complexity Science Hub, Josefstädterstraße 39, Vienna A-1080, Austria;1. Freie Universität Berlin, Germany;2. Johannes Gutenberg-Universität Mainz, Germany |
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| Abstract: | We compute the Wigner measures associated to solutions of semi-classical nonlinear Schrödinger equations. These solutions focus at a point. Outside the caustic, the measures “smooth” the nonlinearity. In the critical cases, a scattering operator describes the jump of Wigner measures at the focus. We show that the problem is ill-posed in terms of Wigner measures. |
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