Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices

An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The star-triangle relation between these systems is introduced, and the Darboux transformations for both linear problems from...

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Bibliographic Details
Published in:Journal of mathematical physics 2007-11, Vol.48 (11), p.1
Main Authors: Doliwa, A., Nieszporski, M., Santini, P. M.
Format: Article
Language:English
Subjects:
Calculus
Exact sciences and technology
Geometry
Laplace transforms
Lattice theory
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
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Summary:An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The star-triangle relation between these systems is introduced, and the Darboux transformations for both linear problems from the Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A geometric interpretation of the Laplace transformations of the self-adjoint 7-point scheme is given and the corresponding novel integrable discrete three-dimensional system is constructed.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2803504