Rational solutions to the ABS list: Degenerating approach
Abstract
In the paper we first construct rational solutions for the Nijhoff-Quispel-Capel (NQC) equation by means of bilinear method. These solutions can be transferred to those of Q3δ equation in the Adler-Bobenko-Suris (ABS) list. Then making use of degeneration relation we obtain rational solutions for Q2, Q1δ, H3δ, H2 and H1. These rational solutions are in Casoratian form and the basic column vector satisfies an extended condition equation set.
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