On one-soliton solutions of the Q2 equation in the ABS list

Abstract

Abstract In this paper, we derive seed and 1-soliton solutions of the Q2 equation in the Adler–Bobenko–Suris list. The seed solutions of Q2 are obtained using those of Q1(δ) $\mbox{Q}1(\delta)$ and an non-auto Bäcklund transformation connecting them. Then using an auto Bäcklund transformation, two types of Q2 one-soliton solutions are obtained based on its seed solutions. These obtained solutions are new and cannot be derived as degenerations from any known soliton solutions.

Keywords

• Soliton solutions
• ABS list
• The Q2 equation
• Bäcklund transformation