Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves. (English) Zbl 1072.35167 Int. Math. Res. Not. 2004, No. 66, 3559-3584 (2004). Small in \(H^1\) solutions are decomposed into solitary and dispersive waves. It is shown that as \(t \rightarrow \infty\), the solitary wave component converges to a fixed solitary wave, and the dispersive component converges strongly in \(H^1\) to a solution of the free Schrödinger equation. Reviewer: Igor Andrianov (Köln) Cited in 2 ReviewsCited in 38 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35B35 Stability in context of PDEs 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems 35Q51 Soliton equations Keywords:NLS equation; soliton; dispersive wave; asymptotic stability; asymptotic completeness PDF BibTeX XML Cite \textit{S. Gustafson} et al., Int. Math. Res. Not. 2004, No. 66, 3559--3584 (2004; Zbl 1072.35167) Full Text: DOI arXiv OpenURL