REVIEW 2 cited by
Discrete Lax pairs and hierarchies of integrable difference systems
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We introduce a family of order $N\in \mathbb{N}$ Lax matrices that is indexed by the natural number $k\in \{1,\ldots,N-1\}.$ For each value of $k$ they serve as strong Lax matrices of a hierarchy of integrable difference systems in edge variables that in turn lead to hierarchies of integrable difference systems in vertex variables or in a combination of edge and vertex variables. Furthermore, the entries of the Lax matrices are considered as elements of a division ring, so we obtain hierarchies of discrete integrable systems extended in the non-commutative domain.
Forward citations
Cited by 2 Pith papers
-
On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps
A symmetry-based construction yields rational Lax matrices for the Lambda, H and F families of quadrirational Yang-Baxter maps, with the FIV map left out because it admits no symmetry.
-
Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions
A single non-abelian system of equations unifies classical and relativistic elastic collisions, and its lattice reinterpretation subsumes both the linear and nonlinear theories of discrete analytic functions.
Discussion (0). Continue with ORCID to comment.