Fractional Volterra Hierarchy

Abstract

The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional generalization of the Volterra lattice hierarchy, so we name it the fractional Volterra hierarchy. In this paper, we give the definition of this integrable hierarchy in terms of Lax pair and Hamiltonian formalisms, construct its tau functions, and present its multi-soliton solutions.

22 pages, 4 figures

References in corpus (2)

• The Extended Bigraded Toda hierarchy
• Hodge-GUE correspondence and the discrete KdV equation

Cited by in corpus (4)

• Hodge-GUE correspondence and the discrete KdV equation
• Hurwitz numbers and integrable hierarchy of Volterra type
• Cubic Hodge integrals and integrable hierarchies of Volterra type
• The Hodge-FVH Correspondence