We consider the nonlinear Klein–Gordon equations coupled with the Born–Infeld theory under the electrostatic solitary wave ansatz. The existence of the least-action solitary waves is proved in both bounded smooth domain case and ${\mathbb{R}}^{3}$ case. In particular, for bounded smooth domain case, we study the asymptotic behaviors and profiles of the positive least-action solitary waves with respect to the frequency parameter ω. We show that when κ and ω are suitably large, the least-action solitary waves admit only one local maximum point. When $\omega \to \infty $, the point-condensation phenomenon occurs if we consider the normalized least-action solitary waves.

@article{AIHPC_2010__27_1_351_0, author = {Yu, Yong}, title = {Solitary waves for nonlinear {Klein{\textendash}Gordon} equations coupled with {Born{\textendash}Infeld} theory}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {351--376}, publisher = {Elsevier}, volume = {27}, number = {1}, year = {2010}, doi = {10.1016/j.anihpc.2009.11.001}, zbl = {1184.35286}, mrnumber = {2580514}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.001/} }

TY - JOUR AU - Yu, Yong TI - Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 351 EP - 376 VL - 27 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.001/ DO - 10.1016/j.anihpc.2009.11.001 LA - en ID - AIHPC_2010__27_1_351_0 ER -

%0 Journal Article %A Yu, Yong %T Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 351-376 %V 27 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.001/ %R 10.1016/j.anihpc.2009.11.001 %G en %F AIHPC_2010__27_1_351_0

Yu, Yong. Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 1, pp. 351-376. doi : 10.1016/j.anihpc.2009.11.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.001/

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