2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115005We consider the time-dependent non linear Schrodinger equations with a double well potential in dimensions d =1 and d=2. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time.Mathematical PhysicsAnalysis of PDEs35Bxx (Primary); 35Q40, 35K55 (Secondary)text