Recently Dabholkar and Vafa proposed that closed string tachyon potential for
non-supersymmetric orbifold \C/\Z_3 in terms of the solution of a tt∗
equation. We extend this result to \C^2/\Z_n for n=3,4,5. Interestingly,
the tachyon potentials for n=3 and 4 are still given in terms of the
solutions of Painleve III type equation that appeared in the study of
\C^1/\Z_3 with different boundary conditions. For \C^2/\Z_5 case, governing
equations are of generalized Toda type. The potential is monotonically
decreasing function of RG flow.Comment: 15 pages, reference added. to appear in PL