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Nonlinear quasimodes near elliptic periodic geodesics

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.

preprint2011arXivOpen access
Pierre AlbinHans ChristiansonJeremy L. MarzuolaLaurent Thomann
math.AP
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Pierre AlbinHans ChristiansonJeremy L. MarzuolaLaurent Thomann

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