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.
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.
@article{AIHPC_2010__27_4_1073_0, author = {Masmoudi, Nader and Nakanishi, Kenji}, title = {From the {Klein{\textendash}Gordon{\textendash}Zakharov} system to a singular nonlinear {Schr\"odinger} system}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1073--1096}, publisher = {Elsevier}, volume = {27}, number = {4}, year = {2010}, doi = {10.1016/j.anihpc.2010.02.002}, mrnumber = {2659158}, zbl = {1197.35244}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2010.02.002/} }
TY - JOUR AU - Masmoudi, Nader AU - Nakanishi, Kenji TI - From the Klein–Gordon–Zakharov system to a singular nonlinear Schrödinger system JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 1073 EP - 1096 VL - 27 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2010.02.002/ DO - 10.1016/j.anihpc.2010.02.002 LA - en ID - AIHPC_2010__27_4_1073_0 ER -
%0 Journal Article %A Masmoudi, Nader %A Nakanishi, Kenji %T From the Klein–Gordon–Zakharov system to a singular nonlinear Schrödinger system %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 1073-1096 %V 27 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2010.02.002/ %R 10.1016/j.anihpc.2010.02.002 %G en %F AIHPC_2010__27_4_1073_0
Masmoudi, Nader; Nakanishi, Kenji. From the Klein–Gordon–Zakharov system to a singular nonlinear Schrödinger system. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 4, pp. 1073-1096. doi : 10.1016/j.anihpc.2010.02.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2010.02.002/
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