Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations

Details Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations

2006-05-08

arxiv.org/abs/nlin/0605021v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages

Scientific paper

In work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants which gave solutions to the cylindrical Toda equations. Later the author considered a more general class of operators which retained some of the properties of those cited and found analogous asymptotics for the determinants. These results applied only in what we call the regular case, when the symbol of an associated convolution operator is nonzero and has zero index. The present work goes further and establishes asymptotics for a class of singular cases.

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