Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory

  • Yong Yu

    Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA

Abstract

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 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 , the point-condensation phenomenon occurs if we consider the normalized least-action solitary waves.

Cite this article

Yong Yu, Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 1, pp. 351–376

DOI 10.1016/J.ANIHPC.2009.11.001