On $\tau$-function of the quadrilateral lattice

Abstract

We investigate the $\tau$-function of the quadrilateral lattice using the nonlocal $\bar{\partial }$-dressing method, and we show that it can be identified with the Fredholm determinant of the integral equation which naturally appears within that approach.

7 pages

Cited by in corpus (2)

• Desargues maps and the Hirota-Miwa equation
• Darboux transformations for linear operators on two dimensional regular lattices