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

References in corpus (7)

• Lax pair for the Adler (lattice Krichever-Novikov) System
• Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach
• Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization
• Symbolic Computation of Lax Pairs of Partial Difference Equations Using Consistency Around the Cube
• Backlund transformations for integrable lattice equations
• Rational Solutions to the ABS List: Transformation Approach
• A variational perspective on continuum limits of ABS and lattice GD equations