2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80609Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish explicitly for single-waves zero-order approximations, and exponentially, outside the wave interaction-region, for multiple-waves. Simple expressions for their asymptotic effects on the solution are obtained.Exactly Solvable and Integrable Systemstext