Global dynamics below excited solitons for the nonlinear Schr\"odinger equation with a potential

Kenji Nakanishi

Global dynamics below excited solitons for the nonlinear Schr\"odinger equation with a potential

Analysis of PDEs 2016-02-11 v2

Authors: Kenji Nakanishi

Abstract

Consider the nonlinear Schr\"odinger equation (NLS) with a potential with a single negative eigenvalue. It has solitons with negative small energy, which are asymptotically stable, and, if the nonlinearity is focusing, then also solitons with positive large energy, which are unstable. In this paper we classify the global dynamics below the second lowest energy of solitons under small mass and radial symmetry constraints.

Keywords

nonlinear schrödinger equation potential solitons global dynamics asymptotic stability radial symmetry excited solitons

Cite

@article{arxiv.1504.06532,
  title  = {Global dynamics below excited solitons for the nonlinear Schr\"odinger equation with a potential},
  author = {Kenji Nakanishi},
  journal= {arXiv preprint arXiv:1504.06532},
  year   = {2016}
}

Comments

43 pages. A gap has been fixed in Section 8 in the case of two non-scattering profiles, with Lemma 7.1 modified and a more general statement (Theorem 7.2)

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