  The Dirac equation on the toroidal surface is studied. The non-constant Fermi
velocity functions are used in the Dirac Hamiltonian to get trigonometric Scarf
and Rosen-Morse potentials using the method given in [19], then, the exact
solutions are written. On the other hand, consecutive mappings are used to get
a trigonometric Scarf I-like potential model and the solutions are obtained in
the second part of the paper.
