no. 2
The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
[Méthode WKB et instabilité géométrique pour les équations de Schrödinger non linéaires sur des surfaces]
Bulletin de la Société Mathématique de France, Tome 136 (2008) no. 2, pp. 167-193

In this paper we are interested in constructing WKB approximations for the nonlinear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.

À l'aide de la méthode WKB nous construisons des solutions approchées à l'équation de Schrödinger cubique sur une variété qui possède une géodésique stable. Cette construction permet d'obtenir des résultats d'instabilités dans des espaces de Sobolev.

DOI : 10.24033/bsmf.2553
Classification : 35Q55, 35B35, 35R25
Keywords: nonlinear schrödinger equation, instability, quasimode
Mots-clés : équation de schrödinger non linéaire, instabilité, quasi-mode 
@article{BSMF_2008__136_2_167_0,
     author = {Thomann, Laurent},
     title = {The {WKB} method and geometric instability for nonlinear {Schr\"odinger} equations on surfaces},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {167--193},
     year = {2008},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {136},
     number = {2},
     doi = {10.24033/bsmf.2553},
     mrnumber = {2415340},
     zbl = {1161.35050},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2553/}
}
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Thomann, Laurent. The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces. Bulletin de la Société Mathématique de France, Tome 136 (2008) no. 2, pp. 167-193. doi: 10.24033/bsmf.2553

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