Fay-like identities of the Toda lattice hierarchy and its dispersionless limit - TEO, LEE-PENG (WORLD SCIENTIFIC PUBL CO PTE LTD, 2006)
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.