Solitary waves in graphene-membrane

Abstract

A two-dimensional crystalline membrane model usually adopted for free-standing monolayer graphene is considered for the search of solitary waves. An extended mean field analysis is performed and small deviations around this mean field exhibit a sinusoidal profile for the membrane. Non-homogeneous configurations are found to have stable localized energy that propagate along a transverse direction, being that their height and width are related to the elastic constants. Upper limits for the velocity of propagation of two different solitary wave solutions are found to be, respectively, of the order of 40 km/s and 100 km/s.