Rational Solutions to the ABS List: Transformation Approach

In the paper we derive rational solutions for the lattice potential modified Korteweg–de Vries equation, and $\mathrm{Q2}$, $\mathrm{Q1}(\delta)$, $\mathrm{H3}(\delta)$, $\mathrm{H2}$ and $\mathrm{H1}$ in the Adler–Bobenko–Suris list. Bäcklund 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.