Communications in Number Theory and Physics
Volume 9 (2015)
Dubrovin-Zhang hierarchy for the Hodge integrals
Pages: 239 – 271
In this paper we prove that the generating series of the Hodge integrals over the moduli space of stable curves is a solution of a certain deformation of the KdV hierarchy. This hierarchy is constructed in the framework of the Dubrovin–Zhang theory of the hierarchies of the topological type. It occurs that our deformation of the KdV hierarchy is closely related to the hierarchy of the Intermediate Long Wave equation.
2010 Mathematics Subject Classification