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, p. 351-376

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 ${ℝ}^{3}$ 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--Gordon equations coupled with Born--Infeld theory},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {1},
year = {2010},
pages = {351-376},
doi = {10.1016/j.anihpc.2009.11.001},
zbl = {1184.35286},
mrnumber = {2580514},
language = {en},
url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPC_2010__27_1_351_0/

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