2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71268We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.20 pages; survey of previous resultsAnalysis of PDEsMathematical PhysicsPrimary: 35Q55; Secondary: 35A05, 35B30, 35B35text