2019/12/31 by Danda Zhang, Dan-Da Zhang, Peter H. van der Kamp +2 · 21 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebra over a field #Component (thermodynamics) #Computer science #Extension (predicate logic) #Mathematics #Numerical methods for differential equations #Physics #Polynomial and algebraic computation #Programming language #Pure mathematics #Quantum mechanics #nlin.SI
paper · pdf · doi:10.3842/sigma.2020.060
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2020/07/01 · openalex publication_date 2020/07/01 · arxiv updated 2020/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Bcklund 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 Painlev equations can also be derived in the context, and the approach extends to N -component generalizations of higher dimensional lattice equations.