Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 078, 24 pages      arXiv:1702.01266
Contribution to the Special Issue on Symmetries and Integrability of Difference Equations

Rational Solutions to the ABS List: Transformation Approach

Danda Zhang and Da-Jun Zhang
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

Received March 21, 2017, in final form September 26, 2017; Published online October 02, 2017

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. 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.

Key words: rational solutions; Bäcklund transformation; Casoratian; ABS list.

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