Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 17 (2021), 093, 19 pages      arXiv:2106.12835      https://doi.org/10.3842/SIGMA.2021.093

A Revisit to the ABS H2 Equation

Aye Aye Cho, Maebel Mesfun and Da-Jun Zhang
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

Received June 25, 2021, in final form October 13, 2021; Published online October 18, 2021

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 continuum limit $S^{(1,0)}$ is related to the eigenfunction in the Lax pair of the Korteweg-de Vries equation.

Key words: H2 equation; consistent around cube; Cauchy matrix approach; continuum limit; KdV equation.

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