Rational solutions to the ABS list: Degenerating approach

2017/03/16 by Song‐lin Zhao, Da‐jun Zhang, Zhao, Song-lin +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1703.05669

openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_δ equation in the Adler-Bobenko-Suris (ABS) list. Then making use of degeneration relation we obtain rational solutions for Q2, Q1_δ, H3_δ, 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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