From the Klein–Gordon–Zakharov system to a singular nonlinear Schrödinger system
Nader Masmoudi
Courant Institute, New York University, 251 Mercer street, New York, NY 10012, USAKenji Nakanishi
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
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Abstract
In this paper, we continue our investigation of the high-frequency and subsonic limits of the Klein–Gordon–Zakharov system. Formally, the limit system is the nonlinear Schrödinger equation. However, for some special case of the parameters going to the limits, some new models arise. The main object of this paper is the derivation of those new models, together with convergence of the solutions along the limits.
Résumé
Dans cet article, on continue l'investigation des limites haute fréquence et subsonique du système de Klein–Gordon–Zakharov. Formellement, le système limite est le système de Schrödinger nonlinéaire. Cependant, pour un cas particulier des paramètres, on trouve un nouveau modèle qui contient un terme singulier. L'objet de ce papier est de donner une dérivation rigoureuse de ce modèle et de montrer la convergence dans l'espace d'énergie.
Cite this article
Nader Masmoudi, Kenji Nakanishi, From the Klein–Gordon–Zakharov system to a singular nonlinear Schrödinger system. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 4, pp. 1073–1096
DOI 10.1016/J.ANIHPC.2010.02.002