  Using perturbation expansion of Maxwell equations, the amplitude equation is
derived for nonlinear TM and TE surface plasmon waves supported by graphene.
The equation describes interplay between in-plane beam diffraction and
nonlinerity due to light intensity induced corrections to graphene conductivity
and susceptibility of dielectrics. For strongly localized TM plasmons, graphene
is found to bring the superior contribution to the overall nonlinearity. In
contrast, nonlinear response of the substrate and cladding dielectrics can
become dominant for weakly localized TE plasmons.
