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 Q3${}_{\delta }$ equation in the Adler-Bobenko-Suris (ABS) list. Then making use of degeneration relation we obtain rational solutions for Q2, Q1${}_{\delta }$, H3${}_{\delta }$, H2 and H1. These rational solutions are in Casoratian form and the basic column vector satisfies an extended condition equation set.

arXiv comment19 pages,Typos corrected

References in corpus (6)

• Bäcklund transformation for the Krichever-Novikov equation
• Notes on solutions in Wronskian form to soliton equations: KdV-type
• Multisoliton solutions to the lattice Boussinesq equation
• Soliton solutions for Q3
• Rational Solutions to the ABS List: Transformation Approach
• Rational Solutions of the H3 and Q1 Models in the ABS Lattice List

Cited by in corpus (1)

• A variational perspective on continuum limits of ABS and lattice GD equations