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arXiv · 1903.11578

Matrix resolvent and the discrete KdV hierarchy

Boris Dubrovin·Di Yang
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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.

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Boris Dubrovin, Di Yang. 2020-03-29. Matrix resolvent and the discrete KdV hierarchy. https://doi.org/10.1007/s00220-020-03770-9

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