Painleve Analysis, Backlund and Cole-Hopf Transformations of the (2+1) and (3+1)-dimensional Burgers Equations

We apply the Painleve analysis to the (2+1) and (3+1) - Dimensional Burgers Equations respectively given by ut + ( 2 F (y, t)) uux = (uxx + uyy) and ut + ( 2 F (y, z, t)) uux = (uxx + uyy + uzz) to determine the Backlund transformations and further deduce their respective Cole - Hopf transformations