  We have shown that a Lagrangian for a torus surface can yield second order
nonlinear differential equations using the Euler-Lagrange formulation. It is
seen that these second order nonlinear differential equations can be
transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using
the position dependent mass approach developed by Mustafa for the classical
systems. Then, we have applied the quantization procedure to the nonlinear
quadratic and Mathews-Lakshmanan equations and found their exact solutions.
