Matrix resolvent and the discrete KdV hierarchy

Dubrovin, Boris; Yang, Di

doi:10.1007/s00220-020-03770-9

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Matrix resolvent and the discrete KdV hierarchy

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Yang, Di
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00220-020-03770-9
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arXiv:1903.11578.pdf
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Citation

Dubrovin, B., & Yang, D. (2020). Matrix resolvent and the discrete KdV hierarchy. Communications in Mathematical Physics, 377(3), 1823-1852. doi:10.1007/s00220-020-03770-9.

Cite as: https://hdl.handle.net/21.11116/0000-0006-BCD7-4

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.