Asymptotics of a Class of Solutions to the Cylindrical Toda Equations
C. A. Tracy, H. Widom
Abstract
The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, qk(t), have the representation qk(t) = log det(I-lambda Kk) - log det(I-lambda Kk-1) where Kk 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 (and with an additional symmetry contraint) they reduce to earlier results for the radial Bullough-Dodd equation.
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