# Rational Solutions to the ABS List: Transformation Approach

## TL;DR

This paper derives rational solutions for several lattice equations from the ABS list using Bäcklund transformations and a unified Casoratian tau function, advancing the understanding of integrable lattice systems.

## Contribution

It introduces a unified approach to obtain rational solutions for multiple ABS lattice equations via Casoratian tau functions and Bäcklund transformations.

## Key findings

- Derived rational solutions for multiple ABS lattice equations.
- Established a unified Casoratian tau function framework.
- Demonstrated the use of Bäcklund transformations in solution derivation.

## Abstract

In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1($\delta$), H3($\delta$), H2 and H1 in the Adler-Bobenko-Suris list. B\"acklund transformations between these lattice equations are used. All these rational solutions are related to a unified $\tau$ function in Casoratian form which obeys a bilinear superposition formula.