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.
