Dubrovin-Zhang hierarchy for the Hodge integrals

Abstract

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.

Final version, 20 pages

References in corpus (2)

• A polynomial bracket for the Dubrovin--Zhang hierarchies
• On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket

Cited by in corpus (4)

• Double ramification cycles and integrable hierarchies
• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs