Orbital stability of semitrivial standing waves for the Klein–Gordon–Schrödinger system
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, p. 315-323

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.

@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},
     publisher = {Elsevier},
     volume = {28},
     number = {2},
     year = {2011},
     pages = {315-323},
     doi = {10.1016/j.anihpc.2011.02.003},
     zbl = {1216.35116},
     mrnumber = {2784074},
     language = {en},
     url = {http://www.numdam.org/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, Volume 28 (2011) no. 2, pp. 315-323. doi : 10.1016/j.anihpc.2011.02.003. http://www.numdam.org/item/AIHPC_2011__28_2_315_0/

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