2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109997In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the nonlinearity, the potential and the datum, we prove that the solution can be decomposed into two parts: the soliton and the term dissipating to infinity.14 pages. to appear in Geometric and Functional AnalysisMathematical Physicstext