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

Kikuchi, Hiroaki

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011), p. 315-323 / Harvested from Numdam

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Résumé

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.

Publié le : 2011-01-01

MR 2784074 | Zbl 1216.35116 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.anihpc.2011.02.003

@article{AIHPC_2011__28_2_315_0,
     author = {Kikuchi, Hiroaki},
     title = {Orbital stability of semitrivial standing waves for the Klein--Gordon--Schr\"odinger system},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {28},
     year = {2011},
     pages = {315-323},
     doi = {10.1016/j.anihpc.2011.02.003},
     mrnumber = {2784074},
     zbl = {1216.35116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2011__28_2_315_0}
}

Kikuchi, Hiroaki. Orbital stability of semitrivial standing waves for the Klein–Gordon–Schrödinger system. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) pp. 315-323. doi : 10.1016/j.anihpc.2011.02.003. http://gdmltest.u-ga.fr/item/AIHPC_2011__28_2_315_0/

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