We demonstrate numerically that armchair graphene nanoribbons can support
vibrational localized states in the form of surface solitons. Such localized states appear through
self-localization of the vibrational energy along the edge of the graphene nanoribbon, and they
decay rapidly inside the structure. We find five types of such solitary waves including in-plane and
out-of-plane edge breathers and moving envelope solitons.