  In this paper, we introduce a new look at Finsler surfaces. Landsberg
surfaces are Finsler surfaces that are solutions of a system of non-linear
partial differential equations. Considering the unicorn's Landsberg problem, we
reduce this system to a single non-linear PDE which we call the Landsberg's
PDE. By making use of the new look of Finsler surfaces, we solve the
Landsberg's PDE and get a class of solutions. Moreover, we show that these
solutions and their conformal transformations are Berwaldain.
