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.

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.

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.

DOI : 10.24033/bsmf.2553
Classification : 35Q55, 35B35, 35R25
Keywords: nonlinear schrödinger equation, instability, quasimode
Mot clés : équation de schrödinger non linéaire, instabilité, quasi-mode 
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     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},
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     publisher = {Soci\'et\'e math\'ematique de France},
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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. http://www.numdam.org/articles/10.24033/bsmf.2553/

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