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Nonlinear quasimodes near elliptic periodic geodesics

By Pierre Albin, Hans Christianson, Jeremy L. Marzuola and Laurent Thomann


We consider the nonlinear Schr\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.Comment: 35 page

Topics: Mathematics - Analysis of PDEs, 35Q55, 35R01, 35C20
Year: 2011
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