Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2007-05-04
J. Math. Phys. 48 (2007) 113506
Nonlinear Sciences
Exactly Solvable and Integrable Systems
15 pages, 6 figures; references added, some typos corrected
Scientific paper
10.1063/1.2803504
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.
Doliwa Adam
Nieszporski Maciej
Santini Paolo Maria
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