Solutions to the non-autonomous ABS lattice equations: Casoratians and bilinearization

TL;DR

This paper bilinearizes non-autonomous ABS lattice equations and derives their solutions in Casoratian form, providing shift formulae for verification, advancing the analytical methods for these integrable systems.

Contribution

It introduces bilinearization and Casoratian solutions for non-autonomous ABS lattice equations, expanding the analytical toolkit for these integrable models.

Findings

Derived Casoratian solutions for non-autonomous ABS equations

Provided shift formulae for solution verification

Enhanced understanding of bilinear structures in lattice equations

Abstract

In the paper non-autonomous H1, H2, H3$_\delta$ and Q1$_\delta$ equations in the ABS list are bilinearized. Their solutions are derived in Casoratian form. We also list out some Casoratian shift formulae which are used to verify Casoratian solutions.