Nonlinear quasimodes near elliptic periodic geodesics

Details Nonlinear quasimodes near elliptic periodic geodesics Nonlinear quasimodes near elliptic periodic geodesics

2011-03-16

arxiv.org/abs/1103.3253v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

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.

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