| We demonstrate numerically that armchair graphene nanoribbons can supportvibrational 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.
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