2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122147We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal surface. We show the existence of both uniform sliding states and periodic travelling waves as well in a two-dimensional sine-Gordon lattice equation using topological and variational methods.29 pages, 3 figures. to appear NonlinearityPattern Formation and Solitonstext