Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential
arXiv:1504.06532
Abstract
Consider the nonlinear Schrödinger 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.
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)