Nonlinear quasimodes near elliptic periodic geodesics
Analysis of PDEs
2011-03-17 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1103.3253,
title = {Nonlinear quasimodes near elliptic periodic geodesics},
author = {Pierre Albin and Hans Christianson and Jeremy L. Marzuola and Laurent Thomann},
journal= {arXiv preprint arXiv:1103.3253},
year = {2011}
}
Comments
35 pages