A Revisit to the ABS H2 Equation

Abstract

In this paper, we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the 𝑆⁽⁰’⁰⁾ and 𝑆⁽¹’⁰⁾ variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of 𝑆⁽⁰’⁰⁾ and 𝑆⁽¹’⁰⁾ in terms of their 3-dimensional consistency, Lax pair, bilinear form, and continuum limits. It is shown that 𝑆⁽¹’⁰⁾itself satisfies a 9-point lattice equation, and in the continuum limit 𝑆⁽¹’⁰⁾ is related to the eigenfunction in the Lax pair of the Korteweg-de Vries equation.