Abstract

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k, have the representation q_k = log det - log det where K_k are integral operators. This class includes the n-periodic cylindrical Toda equations. For n=2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation and for n=3 they reduce to earlier results for the radial Bullough-Dodd equation.