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arXiv · 1103.3253

Nonlinear quasimodes near elliptic periodic geodesics

Pierre Albin·Hans Christianson·Jeremy L. Marzuola·Laurent Thomann
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Abstract

We consider the nonlinear Schrödinger 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 Schrödinger evolution of such a quasimode remains localized near the geodesic, at least for short times.

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Pierre Albin, Hans Christianson, Jeremy L. Marzuola, Laurent Thomann. 2011-03-16. Nonlinear quasimodes near elliptic periodic geodesics. https://arxiv.org/abs/1103.3253

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