Orbital stability of semitrivial standing waves for the Klein–Gordon–Schrödinger system

Hiroaki Kikuchi

doi:10.1016/j.anihpc.2011.02.003

JournalsaihpcVol. 28, No. 2pp. 315–323

Orbital stability of semitrivial standing waves for the Klein–Gordon–Schrödinger system

Hiroaki Kikuchi
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan

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Abstract

In the present paper, we study the orbital stability and instability of standing waves of the Klein–Gordon–Schrödinger system. Especially, we are interested in a standing wave which is expressed by the unique positive solution $w_{1}$ to a certain scalar field equation. By utilizing the property of the positive solution $w_{1}$ , we can apply the general theory of Grillakis, Shatah and Strauss (1987) [11] and show the stability and instability of the standing wave.

Cite this article

Hiroaki Kikuchi, Orbital stability of semitrivial standing waves for the Klein–Gordon–Schrödinger system. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 2, pp. 315–323

DOI 10.1016/J.ANIHPC.2011.02.003