English

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

R2 v1 2026-06-21T17:40:30.726Z