Integrable two-component systems of difference equations

Kamp

2020

SIGMA

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.

“…In [35] certain a-and m-bond systems lead to double H-type vertex systems, cf. [35,Proposition 6.1].…”

Section: Abs Equationsmentioning

confidence: 99%

Section: Abs Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Multi-Component Extension of CAC Systems

Kamp

2020

SIGMA

Journal of Mathematical Physics

“…Apparently, the potential h is invariant under translations, so one speaks for a hidden potential symmetry group of the starting lattice equation (χ 4 ). We postpone to give a detailed analysis on these issues in a future publication, and refer to [15] for a recent account along this line of research for integrable discrete equations on quad-graphs.…”

Section: Discussionmentioning

confidence: 99%

Tetrahedron maps and symmetries of three dimensional integrable discrete equations

Kassotakis

Nieszporski

Papageorgiou

et al. 2019

Self Cite

A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on Z 3 is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter maps, based on the invariants of symmetry groups of the lattice equations. The method is demonstrated by a case-by-case analysis of the octahedron type lattice equations classified recently, leading to some new examples of tetrahedron maps and integrable coupled lattice equations.

“…It turns out that the continuous counterpart of (1.6) consists of the potential KdV equation and the time-part in the Lax pair of the (potential) KdV equation. Note that with some transformations the system (1.6) will be equivalent to a H1 × H2 two-component system which is first derived in [11] (see equation (3.9)). The paper is arranged as follows.…”

Section: Introductionmentioning

confidence: 99%

A Revisit to the ABS H2 Equation

Cho¹,

Mesfun²,

Zhang³

2021

SIGMA

In this paper we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly related to the S (0,0) and S (1,0) variables in the Cauchy matrix scheme. We elaborate the coupled quad-system of S (0,0) and S (1,0) in terms of their 3-dimensional consistency, Lax pair, bilinear form and continuum limits. It is shown that S (1,0) itself satisfies a 9-point lattice equation and in continuum limit S (1,0) is related to the eigenfunction in the Lax pair of the Korteweg-de Vries equation.