  We develop a rigorous quantum-mechanical theory of the nonlinear optical
process of difference frequency generation of surface plasmon-polaritons in
Landau-quantized graphene. Although forbidden in the electric-dipole
approximation, the second-order susceptibility is surprisingly high, equivalent
to the bulk magnitude above $10^{-3}$ m/V. We consider the graphene monolayer
as a nonlinear optical component of a monolithic photonic chip with integrated
pump fields. The nonlinear power conversion efficiency of the order of tens
$\mu$W/W$^2$ is predicted from structures of $10-100$ $\mu$m size. We
investigate a variety of waveguide configurations to identify the optimal
geometry for maximum efficiency.
