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Asymptotic stability of the ground states of the nonlinear Schrödinger equation. (Italian. English summary) Zbl 1006.35088

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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
37N40 Dynamical systems in optimization and economics
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
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