# On reductions of the discrete Kadomtsev--Petviashvili-type equations

## TL;DR

This paper investigates reductions of discrete Kadomtsev--Petviashvili-type equations on algebraic curves, deriving new integrable lattice models and partial difference equations, including extended forms of known equations.

## Contribution

It introduces a unified reduction framework for discrete AKP, BKP, and CKP equations on algebraic curves, leading to new integrable lattice models and partial difference equations.

## Key findings

- Derived unified formulas for reduced integrable lattice equations.
- Produced new extended integrable lattice models such as discrete Sawada--Kotera, Kaup--Kupershmidt, and Hirota--Satsuma.
- Connected reductions to important partial difference equations.

## Abstract

The reduction by restricting the spectral parameters $k$ and $k'$ on a generic algebraic curve of degree $\mathcal{N}$ is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable systems possessing a more general solution structure arise from the reduction, and in each case a unified formula for generic positive integer $\mathcal{N}\geq 2$ is given to express the corresponding reduced integrable lattice equations. The obtained extended two-dimensional lattice models give rise to many important integrable partial difference equations as special degenerations. Some new integrable lattice models such as the discrete Sawada--Kotera, Kaup--Kupershmidt and Hirota--Satsuma equations in extended form are given as examples within the framework.