Multi-Component Extension of CAC Systems

Abstract

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.

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Cited by in corpus (6)

• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Discrete Lax pairs and hierarchies of integrable difference systems
• Integrability of auto-Bäcklund transformations,and solutions of a torqued ABS equation
• Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube
• Local and nonlocal complex discrete and semi-discrete sine-Gordon equations and solutions
• Search for integrable two-component versions of the lattice equations in the ABS-list