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Free keywords:
Mathematical Physics, Mathematics, Nonlinear Sciences, Exactly Solvable and Integrable Systems
Abstract:
Based on the matrix-resolvent approach, for an arbitrary solution to the
discrete KdV hierarchy, we define the tau-function of the solution, and compare
it with another tau-function of the solution defined via reduction of the Toda
lattice hierarchy. Explicit formulae for generating series of logarithmic
derivatives of the tau-functions are then obtained, and applications to
enumeration of ribbon graphs with even valencies and to the special cubic Hodge
integrals are considered.
