2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123415We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations) under a KP-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrödinger equation.26 pages, minor changesAnalysis of PDEstext