Multi-Component Extension of CAC Systems
Danda Zhang, Peter H. van der Kamp, Da‐jun Zhang · Symmetry Integrability and Geometry Methods and Applications · 2020
In this paper an approach to generate multi-dimensionally consistent N -component systems is proposed.The approach starts from scalar multi-dimensionally 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.