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

Abstract

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 3D system is constructed.

15 pages, 6 figures; references added, some typos corrected

References in corpus (3)

• Discrete Riemann Surfaces and the Ising model
• The B-quadrilateral lattice, its transformations and the algebro-geometric construction
• Generalized isothermic lattices

Cited by in corpus (5)

• Darboux transformations for linear operators on two dimensional regular lattices
• Linear problems and Bäcklund transformations for the Hirota-Ohta system
• Solitons of a vector model on the honeycomb lattice
• Explicit solutions for a nonlinear model on the honeycomb and triangular lattices
• Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation