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

Kikuchi, Hiroaki

doi:10.1016/j.anihpc.2011.02.003

Kikuchi, Hiroaki

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 315-323.

corrigé par Erratum

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2011.02.003

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     author = {Kikuchi, Hiroaki},
     title = {Orbital stability of semitrivial standing waves for the {Klein{\textendash}Gordon{\textendash}Schr\"odinger} system},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {315--323},
     publisher = {Elsevier},
     volume = {28},
     number = {2},
     year = {2011},
     doi = {10.1016/j.anihpc.2011.02.003},
     mrnumber = {2784074},
     zbl = {1216.35116},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.003/}
}

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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) no. 2, pp. 315-323. doi : 10.1016/j.anihpc.2011.02.003. http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.003/

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