Generic solutions for some integrable lattice equations

TL;DR

This paper derives general solutions for various integrable lattice equations using $ au$-functions and Miwa's coordinates, unifying multiple hierarchies in a common framework.

Contribution

It introduces a unified approach to solutions of lattice principal chiral, KP hierarchy, and N-wave equations using $ au$-functions and Miwa's coordinates.

Findings

Explicit expressions for $ au$-functions and solutions for lattice equations

Unification of different lattice hierarchies under a common solution framework

Identification of Miwa's coordinates as lattice parameters

Abstract

We derive the expressions for $\psi$-functions and generic solutions of lattice principal chiral equations, lattice KP hierarchy and hierarchy including lattice N-wave type equations. $\tau$-function of $n$ free fermions plays fundamental role in this context. Miwa's coordinates in our case appear as the lattice parameters.