2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94551Multi scales method is used to analyze a nonlinear differential-difference equation. In order $ε^3$ the NLS equation is found to determine the space-time evolution of the leading amplitude. In the next order this has to satisfy a complex mKdV equation (the next in the NLS hierarchy) in order to eliminate secular terms. The zero dispersion point case is also analyzed and the relevant equation is a modified NLS equation with a third order derivative term included6 pages, LaTeX, paper presented at NEEDS'99 Kolymbari, CreteExactly Solvable and Integrable Systemstext