Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

Details Asymptotics of a Class of Solutions to the Cylindrical Toda Equations Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

1997-01-10

arxiv.org/abs/solv-int/9701003v1

Commun. Math. Phys 190 (1998) 697-721

Mathematics

Functional Analysis

29 pages, no figures, LaTeX file

Scientific paper

10.1007/s002200050257

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k(t), have the representation q_k(t) = log det(I-lambda K_k) - log det(I-lambda K_{k-1}) 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 (and with an additional symmetry contraint) they reduce to earlier results for the radial Bullough-Dodd equation.

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