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, p. 1073-1096

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--Gordon--Zakharov system to a singular nonlinear Schr\"odinger system},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {27},
     number = {4},
     year = {2010},
     pages = {1073-1096},
     doi = {10.1016/j.anihpc.2010.02.002},
     zbl = {1197.35244},
     mrnumber = {2659158},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPC_2010__27_4_1073_0/

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