2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74074We construct multi-phase travelling waves which are periodic in time and quasi-periodic in the spatial variable for infinite nonlinear chains with nearest neighbor interactions. The main difficulty in the construction is a small divisor problem. We prove a KAM-type theorem for an infinite dimensional system following the approach of W. Craig and C. E Wayne which was further developed by J. Bourgain.160 pagesClassical Analysis and ODEsMathematical PhysicsDynamical Systems37K60, 34C15text