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

Abstract

The reduction by restricting the spectral parameters $k$ and $k^{\prime }$ 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 $\mathcal{N}\ge 2$ 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.

18 pages

References in corpus (3)

• Direct linearising transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations
• On a discrete analog of the Tzitzeica equation
• Linear integral equations, infinite matrices, and soliton hierarchies

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