Cuccagna, Scipio Asymptotic stability of the ground states of the nonlinear Schrödinger equation. (Italian. English summary) Zbl 1006.35088 Rend. Ist. Mat. Univ. Trieste 32, Suppl. 1, 105-118 (2001). The author presents a panoramic view of the behaviour of the solutions of the nonlinear Schrödinger equation near the ground states. The analysis for \(t\to\infty\) shows asymptotic stability of the ground states for a large family of nonlinearities. The results are similar to those of the integrable systems. Reviewer: Luis Vazquez (Madrid) Cited in 4 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 37N40 Dynamical systems in optimization and economics 37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems Keywords:ground state; stability; integrability; nonlinear Schrödinger equation PDF BibTeX XML Cite \textit{S. Cuccagna}, Rend. Ist. Mat. Univ. Trieste 32, 105--118 (2001; Zbl 1006.35088) OpenURL