The nonlinear TE surface waves guided by an interface of a semi-infinite Kerr-type
dielectric medium and a one-dimensional graphene-based photonic crystal have been investigated
using the transfer-matrix method. It is shown that increasing the intensity of the incident
beam drastically changes dispersion behavior inside the graphene-induced photonic band gap
as a result of nonlinearity. Also regarding the simulation results, it reveals that the peculiar
dispersion that is governed by a nonlinear structure appeared to be tuned by graphene conductivity
via an external electric field. Applying such an electric field makes it possible to easily tune
the nonlinear surface waves at the desired frequency only by adjusting the chemical potential of
the graphene. Also, it is shown that for application purposes, the results of studies can be applied
to the case in which graphene nanolayers are embedded by identical dielectric constant, i.e., zero
permittivity contrast of dielectric.