  From a three-dimensional boundary value problem for the time harmonic
classical Maxwell equations, we derive the dispersion relation for a surface
wave, the edge plasmon-polariton (EP), that is localized near and propagates
along the straight edge of a planar, semi-infinite sheet with a spatially
homogeneous, scalar conductivity. The sheet lies in a uniform and isotropic
medium; and serves as a model for some two-dimensional (2D) conducting
materials such as the doped monolayer graphene. We formulate a homogeneous
system of integral equations for the electric field tangential to the plane of
the sheet. By the Wiener-Hopf method, we convert this system to coupled
functional equations on the real line for the Fourier transforms of the fields
in the surface coordinate normal to the edge, and solve these equations
exactly. The derived EP dispersion relation smoothly connects two regimes: a
low-frequency regime, where the EP wave number, $q$, can be comparable to the
propagation constant, $k_0$, of the ambient medium; and the nonretarded
frequency regime in which $|q|\gg |k_0|$. Our analysis indicates two types of
2D surface plasmon-polaritons on the sheet away from the edge. We extend the
formalism to the geometry of two coplanar sheets.
