A note on the extended dToda hierarchy

Abstract

We give a derivation of dispersionless Hirota equations for the extended dispersionless Toda hierarchy. We show that the dispersionless Hirota equations are nothing but a direct consequence of the genus-zero topological recursion relation for the topological $C{P}^1$ model. Using the dispersionless Hirota equations we compute the two point functions and express the result in terms of Catalan number.

Latex, 16 pages

References in corpus (2)

• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• Two extensions of 1D Toda hierarchy