Multi-Component Extension of CAC Systems

Abstract

In this paper, an approach to generate multidimensionally consistent N-Component systems is proposed. The approach starts from scalar multidimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained N-component systems inherit integrable features such as Bäcklund transformations and Lax pairs, and exhibit interesting aspects, such as nonlocal reductions. Higher-order single-component lattice equations (on larger stencils) and multi-component discrete Painlevé equations can also be derived in the context, and the approach extends to N-component generalizations of higher-dimensional lattice equations.