  In-plane nonlinear delocalized vibrations in uniformly stretched single-layer
graphene (space group P6mm) are considered with the aid of the
group-theoretical methods. These methods were developed by authors earlier in
the framework of the theory of the bushes of nonlinear normal modes (NNMs). We
have found that only 4 symmetry-determined NNMs (one-dimensional bushes), as
well as 14 two-dimensional, 1 three-dimensional and 6 four-dimensional
vibrational bushes are possible in graphene. They are exact solutions to the
dynamical equations of this two-dimensional crystal. Prospects of further
research are discussed.
