2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75411We consider 1D completely resonant nonlinear wave equations of the type v_{tt}-v_{xx}=-v^3+O(v^4) with spatial periodic boundary conditions. We prove the existence of a new type of quasi-periodic small amplitude solutions with two frequencies, for more general nonlinearities. These solutions turn out to be, at the first order, the superposition of a traveling wave and a modulation of long period, depending only on time.20 pages. Corrected some misprints, added a reference, moved Proposition and Lemma 1 from Section 2 to the AppendixAnalysis of PDEs35L05, 35B15, 37K50text