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