Connection between the symmetric discrete AKP system and bilinear ABS lattice equations

Author:

Jing Wang, Da-jun Zhang, Ken-ichi Maruno

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI)

journal:

date:

2023-12-25 00:00:00

Abstract

In this paper, we show that all the bilinear Adler-Bobenko-Suris (ABS) equations (except Q2 and Q4) can be obtained from symmetric discrete AKP system by taking proper reductions and continuum limits. Among the bilinear ABS equations, a simpler bilinear form of the ABS H2 equation is given. In addition, an 8-point 3-dimensional lattice equation and an 8-point 4-dimensional lattice equation are obtained as by-products. Both of them can be considered as extensions of the symmetric discrete AKP equation.

PDF: Connection between the symmetric discrete AKP system and bilinear ABS lattice equations.pdf