Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit

Abstract

In this paper, we derive the Fay-like identities of tau function for the Toda lattice hierarchy from the bilinear identity. We prove that the Fay-like identities are equivalent to the hierarchy. We also show that the dispersionless limit of the Fay-like identities are the dispersionless Hirota equations of the dispersionless Toda hierarchy.

arXiv comment20 pages

References in corpus (9)

• Integrable Hierarchies and Dispersionless Limit
• Integrable Structure of Interface Dynamics
• Conformal maps and dispersionless integrable hierarchies
• Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
• Solution of the dispersionless Hirota equations
• Dispersionless Toda hierarchy and two-dimensional string theory
• Quasi-classical limit of Toda hierarchy and W-infinity symmetries
• On Associativity Equations in Dispersionless Integrable Hierarchies
• Large scale correlations in normal and general non-Hermitian matrix ensembles

Cited by in corpus (9)

• Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy
• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• Auxiliary Linear Problem, Difference Fay Identities and Dispersionless Limit of Pfaff-Toda Hierarchy
• On Addition Formulae of KP, mKP and BKP Hierarchies
• Integrable structure of melting crystal model with two q-parameters
• On the squared eigenfunction symmetry of the Toda lattice hierarchy
• Loewner equations, Hirota equations and reductions of universal Whitham hierarchy
• Darboux transformations and Fay identities for the extended bigraded Toda hierarchy
• 4D limit of melting crystal model and its integrable structure